Composite Structures 132 (2015) 575–583

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Flutter performance of large-scale wind turbine blade with shallow-angled skins Khazar Hayat a, Sung Kyu Ha b,⇑ a b

Dept. of Mech. Eng., The University of Lahore, Main Campus, 1-KM Raiwind Road, Lahore, Pakistan Dept. of Mech. Eng., Hanyang University, 1271, Sa 3-dong, Sangnok-gu, Ansan, Kyeonggi-do 426-791, Republic of Korea

a r t i c l e

i n f o

Article history: Available online 6 June 2015 Keywords: Shallow-angled skins Large-scale blade Classical flutter Aero-elasticity

a b s t r a c t The application of shallow-angled skins with off-axis fiber angle less than 45°, increases the bending stiffness and strength of the large-scale wind turbine blade but reduces its torsional stiffnesses, making it susceptible to the classical flutter instability problem. Single-blade quasi-steady eigenvalue analyses using HAWCStab2 were performed to evaluate the flutter performance of a 5 MW pitch-regulated wind turbine blade with shallow-angled skins configurations. The results showed that the application of shallow-angled skin design concept to the 5 MW blade model does not pose the flutter instability problem. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction The wind turbine market is growing rapidly and has become increasingly competitive. To improve efficiency and cost-effectiveness, the size of utility-scale wind turbines has been increased [1–5]. The use of large-scale turbines with flexible blades increases the risk of dynamic instabilities, particularly classical flutter for pitch-regulated wind turbines. Classical flutter refers to a dynamic unstable condition that, once reached, can lead to catastrophic structural failure [6]. Traditionally, classical flutter has not been an issue for utility-scale horizontal-axis wind turbines (HAWTs) [7]. However, it is expected to become one of the principal design drivers as rotor diameters are continuously increased [4]. The earlier work by Lobitz and Veers on a 20 kW HAWT having blades of 5 m length, shows that the predicted flutter limits were several times the operating speed of wind turbine [8]. In another work on a

Abbreviations: AC, Aerodynamic center; BEM, Blade element momentum theory; BX, Bi-axial; CLT, Classical laminate theory; CG, Center of gravity; CP, Collocation point; DOF, Degree of freedom; EA, Elastic axis; HAWTs, Horizontal-axis wind turbines; HEC, Higher education commission; LE, Leading edge; LHS, Left hand side; MLTM, Ministry of land, transportation and maritime affairs; MW, Mega Watt; NACA, National Advisory Committee for Aeronautics; NCF, Non-crimp fabrics; NREL, National renewable energy laboratory; PS, Pressure side; RHS, Right hand side; SNL, Sandia National Laboratories; SS, Suction side; TE, Trailing edge; TX, Tri-axial; UD, Unidirectional. ⇑ Corresponding author. Tel.: +82 31 400 5249; fax: +82 31 407 1034. E-mail address: [email protected] (S.K. Ha). http://dx.doi.org/10.1016/j.compstruct.2015.05.073 0263-8223/Ó 2015 Elsevier Ltd. All rights reserved.

MW-sized wind turbine blade, Lobitz confirmed that the flutter speed computed from quasi-steady aerodynamics is conservative than that estimated using unsteady (Theodorsen) aerodynamics [9]. Investigations by Hansen [10,11] demonstrated that the single-blade and full-turbine analyses for a wind turbine produce similar flutter predictions, suggesting that the single-blade flutter analysis is adequate. Using single-blade flutter analyses of a MW-sized wind turbine blade, Hansen also showed that lowering the torsional stiffness and shifting the center of mass towards the trailing edge decreases the flutter speed limit [11]. There have been other similar findings that decreasing the torsional frequency decreases the flutter limit [10–12]. This work focuses on predictions of the flutter limit of a 5 MW wind turbine blade with shallow-angled skins. Two shallow-angled symmetric and asymmetric skin configurations (as detailed in Section 2.2) with 35° and 25° off-axis fiber angles were previously proposed in [13], based on the observation that considering the slenderness of the large-scale blade the conventional 45° off-axis fiber angle of the blade skins is not optimal. The shallow-angled skins were evaluated by their application to a utility-scale variable-speed and collective-pitch controlled 5 MW wind turbine blades, in terms of tip deflection, modal frequencies, buckling load factor and strength failure index. The results demonstrated that the application of shallow-angled skins improves the bending stiffness and strength of the blade, accompanied with a reduction of torsion stiffness. The increased bending stiffness and strength of the blade with shallow-angled skins were then reduced to match that of the blade with the conventional 45°-angled skins by thinning the spar

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caps. Consequently, the blade overall mass was lowered while meeting the stiffness, strength and buckling stability requirements. The reduced torsional stiffness of blade with shallow-angled skins increases its susceptibility to the potential danger of classical flutter instability; thus, needs to be evaluated in greater detail. This paper begins with a brief discussion of the theoretical background on the classical flutter instability mechanism, and then discusses the development of a 5 MW wind turbine blade with implemented the shallow-angled skins design concept. The verification of the eigenvalue flutter analysis approach using HAWCStab2 is then presented, followed by the results and discussion section, and finally conclusions are presented. 2. Classical flutter instability mechanism Classical flutter refers to a violent unstable dynamic condition in which the blade structure under the influence of incident aerodynamic loads undergoes the high-amplitude vibrations due to the coupling of the flapwise and torsional modes. Below the flutter limit, the blade response is stable, and vibrations are dampen out by the structural damping. Upon reaching the flutter limit, however, the vibrations start to grow exponentially in the amplitude. Beyond the flutter limit, the blade response becomes unstable because of negative aero-elastic damping, and high-amplitude vibrations become self-exciting and sustainable, subsequently, leading to rapid structure failure [6,14–16]. To understand classical flutter, the instability mechanism of a simple blade section model, taken from Ref. [16], is discussed here. Fig. 1 shows a typical blade section, consisting of two degrees-of-freedom (DOFs), subjected to quasi-steady aerodynamic lift. The incident wind inflow is parallel to the blade chord c. The flapwise translation DOF, denoted by h, is perpendicular to the wind inflow direction, and the torsional rotation DOF, denoted by h, is about the elastic axis (EA). The elastic axis is located at a distance caCG in front of the blade center of gravity (CG). The aerodynamic lift force L is acting at the aerodynamic center (AC), located at a distancecaAC in front the elastic axis. The linear equations of motion of the blade section are:

€  mcaCG €h þ k h ¼ L mh f € þ mðc2 r2 þ c2 a2 Þ€h þ kt h ¼ caAC L;  mcaCG h CG CG

L¼

1 qcW 2 C L ðaÞ; 2

where q is the air density, W is the relative inflow wind speed, and C L is the lift coefficient evaluated at the angle of attack a. To include the torsional velocity h_ effects, the angle of attack is defined at the collocation point (CP), located at the blade three-quarter chord length. The relative wind speed and the angle of attack are therefore:

W¼

"   # qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi W 0 sin h  h_  c 12  aAC h_ ; W 20 þ h_ 2 and a ¼ arctan W 0 cos h ð3Þ

where W 0 is the steady-state relative inflow wind speed. By inserting W and a into Eq. 2, and linearization about h ¼ h_ ¼ h_ ¼ 0, results in the linear approximation to the aerodynamic lift force L:

"   _# h_ 1 1 ch 2 0 ; L  L0 þ cqW 0 C L h    aAC W0 W0 2 2

where m is the mass per unit length of the blade section, r CG is the radius of gyration about the center of gravity normalized by the € and € blade chord length, h h are derived by taking twice time-derivatives of the flapwise translation and the torsional rotation DOFs, and kf and kt represents the flapwise and torsional stiffnesses. When the apparent mass terms is neglected, the quasi-steady aerodynamic lift force L per unit length becomes,

ð4Þ

where L0 is the steady-state lift force, and C 0L represents lift gradient (i.e. C 0L ¼ dC L =daÞ evaluated at the angle of attack a0 ¼ 0. For thin airfoils, the value of C 0L is assumed to be 2p. The steady-state lift can be ignored as it has little influence on the airfoil instability. Thus, Eqs. (1) and (4) can be written in matrix form as:

€ þ Cx_ þ Kx ¼ 0; Mx

ð5Þ T

where the vector x ¼ ½h=c; h consists of non-dimensional DOFs. The blade structure mass matrix M, aerodynamic damping matrix C, and aero-elastic stiffness matrix K are:

M¼

 "

K¼

1

aCG

aCG

r 2CG þ a2CG

 ;

x2f

j

0

r 2CG x2t  jaAC

where xf ¼ flapwise

ð1Þ

ð2Þ

#

" cj 1 C¼ W 0 aAC

#  aAC   ; aAC 12  aAC 1 2

ð6Þ

;

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffi kf =m and xt ¼ kt =ðmc2 r 2CG Þ are the frequencies of

and

torsional

modes

without

inertial

coupling

ði:e: aCG ¼ 0Þ, and j ¼ ðq=2mÞW 20 C 0L is the aerodynamic stiffness. Ignoring the aerodynamic damping matrix C and inserting the assumed solution x ¼ v ekt into Eq. (5) results in the following single-blade eigenvalue problem:

 2  k M þ K v ¼ 0:

ð7Þ

Non-trivial solution of Eq. (7) leads to the following characteristic equation: h i    r2CG k4 þ r2CG þ a2CG x2f þ r2CG x2t  jðaAC þ cCG Þ k2 þ x2f r2CG x2t  jaAC ¼ 0:

ð8Þ

Fig. 1. Typical blade section with two degrees of freedom, reproduced from [16].

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When the real part of the solution of Eq. (8) is positive, this corresponds to unstable behavior; if it is negative, this corresponds to stable behavior. Based on the Routh-Hurwitz criteria [16–18], the following flutter criterion can be deduced from Eq. (8):

q 2m

W 20 C 0L < x2f

r 2CG þ a2CG r 2CG þ x2t aAC þ aCG aAC þ aCG

for aAC þ aCG P 0:

ð9Þ

If the left-hand-side (LHS) of Eq. (9) is greater than the right-hand-side (RHS), then there is considered to be a danger of flutter instability. Based on Eq. (9), the following four main criteria must be met for flutter instability to arise: First, there must be attached flow (i.e. C 0L > 0Þ. If this is not the case, blade torsion rotation will not lead to increased aerodynamic lift. Second, the tip speed must be high; this means that the relative wind speed W 0 must be rather high so that the aerodynamic forces are large enough to overcome the structure elastic forces and leading to classical flutter instability. Third, there must be low flap and torsional stiffnesses, making the flapwise mode frequency xf and torsional mode frequency xt low enough so that they can couple. Fourth, the location of the CG must be aft of the AC (i.e. aAC þ aCG > 0Þ, ensuring the correct phasing between the flapwise and torsional modes of the flutter. In order to study the effects of the bending and torsional stiffness properties on the flutter criterion of a blade section with two DOFs, the flutter criterion, represented by Eq. (9), can be rearranged as follows:

2 W 0 = xf R2 P1  ðc2 =c1 Þ ðc2 =c3 Þ xt qC 0L r 2 þ a2CG r 2CG where R ¼ ; c1 ¼ ; c2 ¼ CG ; c3 ¼ : xf 2m aAC þ aCG aAC þ aCG

577

(UD) laminate was used for spar cap and TE reinforcement. Foam core was used for LE panels and aft panels, and for TE reinforcement regions and shear webs. Gelcoat was added on top of the external TX skin as a protective coating, and an extra epoxy resin was applied to ensure a realistic weight. For brevity purpose, the thickness distributions of the BX skin, Gelcoat and extra resin are not presented. To implement the shallow-angled skins design concept, a ply-level layup was developed, because for the parent SNL 100-00 blade, only the laminate stiffness properties were described in the Sandia report [4]. A laminate is made of UD plies oriented at various fiber angles; therefore, the UD ply stiffness properties can be back-calculated from the laminate stiffness properties using classical laminate theory (CLT). Table 1 lists the various mixing ratios of the UD plies that provided the equivalent UD, BX and TX non-crimp fabrics (NCF) laminate stiffness properties. Table 2 lists the back-calculated UD ply longitudinal, transverse and shear stiffness properties, denoted respectively by Ex, Ey and Exy, respectively. Further information regarding the development of the ply-level layup of the downscaled 5 MW blade can be found in [13]. Fig. 4 shows the computed locations of the AC and the CG, and the stiffness, mass and inertia properties along the blade length. The estimated mass of the downscaled 5 MW blade was approximately 28,721 kg. 2.2. Implementation of shallow-angled skins design concept



ð10Þ

Eq. (10) is in parabolic form, representing the relation between the relative wind speed W 0 and the frequency ratio R for a given flapwise bending mode frequency xf . 2.1. Development of a 5 MW blade A model 5 MW wind turbine blade of length 61.5 m, shown in Fig. 2, was developed by downscaling the geometry and composite layup of the reference 13.2 MW wind turbine blade of length 100 m, titled as SNL 100-00, developed by Sandia National Laboratories, USA [13]. The composite layup, geometry (i.e. chord, pitch-axis and twist angle and web locations), and mass and stiffness properties of the SNL 100-00 blade is well documented in Ref. [4]. Fig. 3(a) shows the cross section of the downscaled blade that is made of two pressure-side (PS) and suction-side (SS) surfaces, each consisting of a leading-edge (LE) panel, spar cap, aft panel and trailing-edge (TE) reinforcement regions, and having two shear webs fitted between them. Fig. 3(b)–(e) shows the downscaled layup thickness distributions. Tri-axial (TX) skins were used for the blade’s internal and external skins and root reinforcement; biaxial (BX) skin was used for shear webs only. Unidirectional

The shallow-angle skins design concept describes that only that the off-axis fibers of the external and internal TX NCF skins on the PS and the SS of the downscaled 5 MW blade had shallow angles of less than 45°, and the rest of the layup remained unchanged for the root buildup, spar caps, shear webs, LE panel, aft-panel, and TE reinforcement regions, as well as for the extra resin layer and the Gelcoat protective coating. Two shallow-angled skin configurations were investigated: symmetric and asymmetric skins, as shown in Fig. 5(a). For the symmetric skin configuration, shallow-angled skins were applied to both the PS and SS. For the asymmetric skin configuration, the shallow-angled skin was applied to only the PS; the SS skin was conventionally 45°-angled. Table 3 lists the cases used to evaluate both skin configurations. For the shallow-angled symmetric skins, the conventional 45° off-axis fiber angle hf of both PS and SS skins was changed to 35° and 25°, and similar changes were made to only the PS skin of the shallow-angled asymmetric skins [13]. The shallow-angled skins increased the blade bending stiffness and strength, accompanied with a reduction in torsion stiffness. The increased stiffness and strength were then lowered by thinning the spar caps, resulting in a 8% and 13% decrease in the blade overall mass (see Table 3) for both skin configurations at 35° and 25° off-axis fiber angles, while meeting the all design requirements [13]. Fig. 5(b)–(d) demonstrates the effects of shallow-angled skins on the blade stiffness properties, computed in terms of the

Fig. 2. Plan-form of the downscaled 5 MW blade, reproduced from [13].

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Fig. 3. Composition of the downscaled 5 MW blade: (a) cross-sectional view; layup thickness distributions of (b) TX internal and external skins, (c) TX root reinforcement, (d) UD spar cap and UD trailing-edge reinforcement, and (e) foam core, reproduced from [13].

Table 1 UD ply mixing ratios to estimate the equivalent laminate stiffness properties, reproduced from [13]. NCF laminate

UD BX TX

Angle-ply contribution [%] 0°

45°

45°

90°

95 – 50

– 50 25

– 50 25

5 – –

stationary mode frequencies. The increase in bending stiffnesses for both skin configurations is evident by the increase in the frequencies of 1st flapwise and 1st edgewise bending modes, represented by solid lines in Fig. 5(b) and (c), at the shallow angles. The 1st flapwise and 1st edgewise bending mode frequencies increased by 2.2% and 3.7%, respectively, for the symmetric skins, and 1.2% and 1.7% for the asymmetric skins at a 25° off-axis fiber angle. On the other hand, the reduction in torsion stiffness is evident by the decrease in the blade 1st torsion mode frequency, represented by solid lines in Fig. 5(d), at shallow angles. At a 25° off-axis fiber angle, the torsion mode frequency lowered by 6.3% and 3.7% for the symmetric and asymmetric skins, respectively. The increase in bending stiffness and the decrease in torsion stiffness for the symmetric skins is higher than that of the asymmetric skins, because shallow-angled skins are applied to both PS and SS of the blade.

The increased bending stiffness of the blade with shallow-angled skins was then reduced to match that of the blade with the conventional 45°-angled skins by reducing the thickness of spar caps. For the blade with reduced mass, the 1st flapwise bending mode frequency (represented by dotted lines in Fig. 5(b)) and the 1st torsion mode frequency (represented by dotted lines in Fig. 5(d)) decreased at the shallow angles. The decrease in the flapwise bending stiffness due to reduced spar cap thickness was not fully compensated for by the increased flapwise bending stiffness caused by shallow-angled skins. Consequently, the overall flapwise bending stiffness of the blade was lowered. The 1st flapwise bending mode frequencies decreased by 7.9% and 7.2% for the symmetric and asymmetric skins, respectively, at a 25° off-axis fiber angle. Since spar cap also contribute to the torsional stiffness, therefore, due to reduced spar cap thickness and use of shallow-angled skins, resulted in higher decrease in the torsional stiffness. The 1st torsion mode frequencies decreased by 16.1% and 12.8% for the symmetric and asymmetric skins, respectively, at a 25° off-axis fiber angle. However, the 1st edgewise mode frequency increased at shallow angles (represented dotted lines in Fig. 5(c)), because the thickness of UD laminates in the spar caps was lowered only which affected the flapwise bending stiffness. The 1st edgewise bending mode frequencies increased by 10.9% and 8.3% for the symmetric and asymmetric skins, respectively, at a 25° off-axis fiber angle. 3. Prediction of flutter limits 3.1. Single-blade Eigenvalue analysis

Table 2 Computed UD ply stiffness properties, reproduced from [13]. Material

Density (kg/m3)

Stiffness [GPa] Ex

Ey

Exy

E-glass/Epoxy (1 mm thick)

1920

43.2

12.6

4.2

Poisson ratio

0.28

In this work, the flutter limits of the downscaled 5 MW blade with shallow-angled skins were predicted using the single-blade quasi-steady eigenvalue flutter analysis, as it is sufficient and convenient to compute the flutter limits and relevant participating modes [11,12]. It should be noted that for eigenvalue flutter

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Fig. 4. Properties of the downscaled 5 MW blade: (a) locations of the AC and CG; (b) cross-sectional stiffnesses; (c) mass and inertial properties.

Fig. 5. (a) Implementation of shallow-angled TX skins, (b) 1st flapwise bending mode, (c) 1st edgewise bending mode, and (d) 1st torsion mode.

Table 3 Cases considered for the blade with the shallow-angled skins, reproduced from [13]. Case description

TX skin off-axis fiber angle [°]

Mass reduction by thinning spar caps [%]

PS

SS

Baseline

45

45

–

Symmetric skins

35 25

35 25

8 13

Asymmetric skins

35 25

45 45

8 13

problem, the nonlinear aeroelastic model of a wind turbine is linearized about a steady-state equilibrium, and this approach is helpful to figure out which modes participate in causing the instability. For the eigenvalue flutter analysis, HAWCStab2 was used [10,11,19]. HAWCStab2 uses Timoshenko beam elements with 6 DOFs per node, and is used for analyzing the aeroelastic response of a wind turbine at any operating condition under the action of aerodynamic forces. Consequently, the elastic structure of downscaled 5 MW blade with shallow-angled skins was modelled using 19 beam elements. The incident aerodynamic forces were computed at the aerodynamic center of each beam element distributed

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along the blade span, using the quasi-steady blade element momentum (BEM) theory. For the single-blade quasi-steady flutter analysis, the turbine rotor ‘‘run-away’’ condition was modelled. To simulate the runaway condition, it was assumed that the turbine was disconnected from the power grid; that the generator’s counter torque was zero, allowing the rotor blade to spin freely; and that the blade pitch setting was zero, thereby ensuring attached flow conditions. Thus, there was nothing to resist the spinning rotor directly facing the incoming wind. In such conditions, the rotor accelerates until it is rotating fast enough for the aerodynamic drag forces to balance the lift forces; that is to say, until the aerodynamic torque is reduced to zero. Thus, for the single-blade eigenvalue flutter analysis, the aero-elastic mode frequencies and damping ratios were computed by varying the rotation speeds of the zero-pitched blade at various steady wind conditions in such a way that the aerodynamic torque becomes zero. The flutter limits were then estimated in terms of the rotor rotation speeds for which the computed aero-elastic damping ratios of any participating mode became negative. 3.2. Verification of single-blade Eigenvalue approach To verify the single-blade eigenvalue analysis using HAWCStab2, the flutter limits of the NREL 5 MW wind turbine blade were computed and compared to the results reported in literature [20]. Table 4 lists the NREL 5 MW blade characteristics in terms of stationary mode frequencies. Fig. 6(a) and (b) shows the eigenvalue analysis results that flutter occurs due to the coupling of the third flapwise and first torsional modes. The aeroelastic frequencies of the third flapwise mode (dotted line with circle markers) and the first torsional mode (dotted line with triangular markers) approached each other, and instability was caused by the negative aeroelastic damping of the third flapwise mode. The rotor speed corresponding to the onset of flutter was approximately 22.3 RPM. The computed flutter limit from the single-blade eigenvalue analyses is close to the range of 24– 27 RPM predicted for the NREL 5 MW blade rotating in still air, based on single-blade and full-turbine eigenvalue analyses [16]. 4. Results and discussion 4.1. Effect of stiffness properties on flutter limit Before the flutter performance of the downscaled 5 MW blade with shallow-angled skins was evaluated using eigenvalue analyses, the effects of the bending and torsional stiffness properties on the flutter criterion of a blade section with two degrees of freedom, derived in Section 2, were qualitatively studied. To plot the flutter criterion (Eq. (9)), a prismatic un-twisted blade section with 1 m chord and 10 m length, and having aerodynamic shape defined by the NACA 6418 airfoil was considered (see Fig. 7(a)). The blade had 10 mm thick BX: ½þhf =  hf S skins on the PS and SS, where hf is the off-axis fiber angle in degrees. The material properties listed in Table 2 were used to compute the blade stiffness properties, in terms of the frequencies of 1st bending and 1st torsional stationary modes, represented by xf and xt , at

Table 4 Computed mode frequencies of NREL 5 MW blade using ADAMS. Mode frequency (Hz)

1st flapwise bending

1st edgewise bending

1st torsion

0.47

1.08

5.53

the off-axis fiber angle hf of 45°, 35° 25°, and 15°. For the baseline case (i.e. hf ¼ 45 ), the computed values of xf and xt were 0.90 Hz and 20.39 Hz. It can be clearly observed in Fig. 7(b) that the xf increases and xt decreases when the conventional 45° off-axis fiber angle of BX skins is changed to the shallow angles of 35°, 25°, and 15°. For the purposes of plotting the flutter criterion, represented by Eq. (9), the air density q of 1.225 kg/m3, the computed blade section mass m of 39.51 kg/m and the radius of gyration r cg of 0.06 m were used. The aerodynamic center aac and center of gravity acg were assumed to be located at distances 25% and 50% of the chord length from the leading edge; and for the attached flow condition, the value of 2p radians was used for the derivative of the lift coefficient curve C 0L . It was assumed that the ratio of torsional stiffness to torsional mode frequency remains constant, when off-axis fiber angle of BX skin is changed from conventional 45° to shallow angles of 35°, 25°, and 15°, thus, the blade radius of gyration remained unchanged. Fig. 7(c) shows parabolic flutter curves plotted for the 45°, 35°, 25°, and 15° off-axis fiber angles of the BX skins, represented by a solid-, dash-, dotted- and dot-dash-line, respectively. Each curve is plotted using a computed value of xf at the off-axis fiber angles of BX skins, and demonstrates a relationship between the flutter speed W 0 and the frequency ratio R. Each curve defines a flutter boundary; the regions below and above a flutter boundary curve correspond respectively to stable and unstable blade conditions. Along each curve, the W 0 decreases with the decrease in the R value, and thereby reducing the flutter limit. The R value is lowered by decreasing the 1st torsional mode frequency xt value, as the 1st bending mode frequency xf value along the curve remains unchanged. On the other hand, the stable region below each curve increased due to the increase in the bending stiffness that arose from decreasing the off-axis fiber angle of the BX skins from the conventional 45° to the shallow angles of 35°, 25°, and 15°, and thereby increasing the flutter limit. The decrease in flutter speed due to the reduction in torsion frequency was not fully compensated for by increase in flutter speed due to the increased flapwise bending frequency arising from the use of shallow off-axis fiber angles; thus, the overall blade flutter limit was lowered when the shallow-angled skins design concept was implemented. Fig. 7(d) shows the flutter speed limits estimated from the plotted flutter curves (shown in Fig. 7(c)) using the computed 1st bending and 1st torsion mode frequencies (shown in Fig. 7(b)) at the off-axis fiber angles of 45°, 35°, 25°, and 15°. The estimated flutter speed for the baseline case (i.e. hf ¼ 45 ) was 7.83 m/s. For the 35° off-axis fiber angle, there was a slight reduction of 3% in flutter speed, because the variation in 1st bending and 1st torsional mode frequencies was not that significant. However, for the shallower angles of 25° and 15°, the flutter speed decreased almost in a linear manner. At a 15° off-axis fiber angle, there was approximately 25% reduction in the flutter speed. The results show that the use of shallow-angled skins increases the blade bending stiffness along with a reduction in torsional stiffness. For a wind turbine blade, the torsional stiffness should be sufficient to avoid any likely risk of aero-elastic flutter instability due to coupling of the flap-wise bending and the torsional modes. Therefore, the use of very low, shallow-angles (less than 25°) may not be appropriate. 4.2. Flutter limits of downscaled 5 MW blade with shallow-angled skins Table 5 lists the characteristics of the downscaled blade that were used for flutter analyses. The blade belongs to an upwind,

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Fig. 6. For NREL 5 MW blade, (a) computed aeroelastic frequencies and (b) damping ratios (b) from the single-blade quasi-steady eigenvalue analysis using HAWCStab2.

Fig. 7. (a) Prismatic blade section with BX skins, (b) mode frequencies, and (c) flutter limit plots, and (d) Flutter speed at shallow off-axis fiber angles.

Table 5 Characteristics of the downscaled wind turbine rotor blade. Rating Blade length [m] Hub radius and hub height [m] Pre-cone and tilt [°] Rated speed [RPM] Cut-in, rated and cut-out winds [m/s]

5 MW 61.5 1.5, 90 2.5, 5 12.1 3, 11.4, 25

3-bladed, variable-speed-regulated and collective-pitch-regulated 5 MW wind turbine rotor that reaches a rated speed of 12.1 RPM at the rated wind of 11.4 m/s. Information regarding other wind turbine components such as the tower, hub, and nacelle can be found in [13,20].

For eigenvalue flutter analysis, the aeroelastic mode frequencies and damping ratios were computed for the cases listed in Table 3 describing the shallow-angled skins design concept, with and without mass reduction included. Fig. 8(a) and (b) shows the first six aeroelastic mode frequencies and damping ratios estimated for the baseline case of downscaled 5 MW blade with skins having conventional 45° off-axis fiber angle. Flutter instability was caused by the possible coupling of the third flapwise (dotted line with circular markers in Fig. 8(a)) and first torsional modes (solid line with triangular markers in Fig. 8(a)), because the frequencies of the third flapwise and first torsional modes approached each other, and the third flapwise mode was negatively damped (dotted line with circular markers in Fig. 8(b)). Similar results were observed for the other cases listed in Table 3, but are not shown for brevity. For the baseline case, the computed flutter speed was approximately 38.42 RPM from the eigenvalue analysis; this speed is

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Fig. 8. For the baseline case of downscaled 5 MW blade, (a) computed aeroelastic frequencies and (b) damping ratios (b) from the single-blade quasi-steady eigenvalue analysis using HAWCStab2.

Fig. 9. Effect of shallow-angled skins on the blade flutter limit: (a) without mass reduction, (b) with mass reduction by thinning spar caps.

approximately 3.17 times the wind turbine rotor rated speed of 12.1 RPM. The predicted flutter speeds for the downscaled 5 MW blade are higher in magnitude than the flutter limits of the NREL 5 MW blade, due to the downscaled blade’s relatively higher bending and torsional stiffness properties. It must also be noted the layup of the parent blade SNL 100-00 is not optimally designed [4]. Similar to the results for a prismatic blade section with shallow-angled skins (discussed in Section 4.1), the overall flutter limit of the downscaled 5 MW blade decreased for the cases listed in Table 3 describing the shallow-angled design concept, with and without mass reduction included. For the blade with shallow-angled skins and without any mass reduction, the flutter limit decreased by 2% and 14% for the symmetric skins, and 1% and 11% for the asymmetric skins at the shallow off-axis fiber angles of 35° and 25°, respectively, as shown in Fig. 9(a). The computed factor of safety for both skins at 25° off-axis fiber angle was 2.71–2.80, demonstrating a moderate decreases the flutter limit. Fig. 9(b) shows the flutter results at shallow-off axis fiber angles when the increased bending stiffness and strength were used to lower the blade mass by thinning the spar caps. The flutter limit

decreased by 19% and 27% for the symmetric skins, and 18% and 24% for the asymmetric skins at the shallow off-axis fiber angles of 35° and 25°, respectively. Although, there is a significant reduction in the flutter limit, but blade was safe because the computed flutter factor of safety in this case was 2.30–2.40 for both skin configurations at a 25° off-axis fiber angle. 5. Conclusions The effect of increased bending stiffness and reduced torsional stiffness due to the use of shallow-angled skins design concept, upon the flutter limit of a prismatic blade section with 2 DOFs was qualitatively studied. The flutter limit decreased due to the decreased torsional stiffness, whereas upward shifting of the flutter boundary occurred due to the increased bending stiffness, resulting in an increase in the flutter limit. However, the reduction in the flutter stability limit due to reduced torsion frequency was not fully compensated for by the increase in the flutter limit due to the increased bending stiffness; thus, the use of the shallow-angled skins design concept resulted in an overall reduction in the blade flutter limit.

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For the downscaled 5 MW pitch-regulated wind turbine blade with shallow-angled skins, the single-blade quasi-steady eigenvalue analyses results showed a moderate decrease of 11–14% for the both symmetric and asymmetric skins at a 25° off-axis fiber angle. The flutter limit of the blade, for which the increased bending stiffness due to shallow-angled skins design concept were used to lower the blade mass by thinning the spar caps, decreased by 24–27% for the 25°-angled skins. However, the blade was safe because the computed factor of safety was 2.30–2.40 times higher than the blade rated RPM of 12.1. Thus, vulnerability to classical flutter instability does not seems to cause a problem for the current downscaled 5 MW blade model with the shallow-angled skins. Acknowledgments The authors would like to thank Mr. Lars Christian Henriksen and Mr. Taeseon Kim, from Department of Wind Energy, Technical University of Denmark, for their technical assistance regarding use of HAWCStab2. Financial support for this research was provided by the Higher Education Commission (HEC), Pakistan, and a grant from the LNG Plant R&D Center, funded by the Ministry of Land, Transportation and Maritime Affairs (MLTM) of the Korean government. References [1] Griffin DA. Blade system design studies volume I: composite technologies for large wind turbine blades, SAND2002-1879, Sandia National Laboratories, Albuquerque, NM, 2002. [2] Veers PS, Ashwill TD, Sutherland HJ, Laird DL, Lobitz DW, Griffin DA, et al. Manufacture and evaluation of wind turbine blades. Wind Energy 2003;6:245–59.

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