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Effects of torsional degree of freedom, geometric nonlinearity, and gravity onaeroelastic behavior of large-scale horizontal axis wind turbine blades under varyingwind speed conditionsMin-Soo Jeong, Myung-Chan Cha, Sang-Woo Kim, In Lee, and Taeseong Kim
Citation: Journal of Renewable and Sustainable Energy 6, 023126 (2014); doi: 10.1063/1.4873130 View online: http://dx.doi.org/10.1063/1.4873130 View Table of Contents: http://scitation.aip.org/content/aip/journal/jrse/6/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Unsteady vortex lattice method coupled with a linear aeroelastic model for horizontal axis wind turbine J. Renewable Sustainable Energy 6, 042006 (2014); 10.1063/1.4890830 A numerical investigation of the stall-delay phenomenon for horizontal axis wind turbine AIP Conf. Proc. 1493, 389 (2012); 10.1063/1.4765518 Dynamic stall analysis of horizontal-axis-wind-turbine blades using computational fluid dynamics AIP Conf. Proc. 1440, 953 (2012); 10.1063/1.4704309 Power performance of canted blades for a vertical axis wind turbine J. Renewable Sustainable Energy 3, 013106 (2011); 10.1063/1.3549153 Aeroelastic Problems of Wind Turbine Blades AIP Conf. Proc. 1281, 1867 (2010); 10.1063/1.3498270
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Effects of torsional degree of freedom, geometricnonlinearity, and gravity on aeroelastic behavior oflarge-scale horizontal axis wind turbine blades undervarying wind speed conditions
Min-Soo Jeong,1 Myung-Chan Cha,2 Sang-Woo Kim,3 In Lee,4,a) andTaeseong Kim5
1Body Durability CAE Team, Research & Development Division, Hyundai Motor Co.,Hwaseong 445-706, South Korea2Ship Performance Research Department II, Hyundai Maritime Research Institute,Hyundai Heavy Industries Co. Ltd., Ulsan 682-792, South Korea3Launch Complex Team, KSLV-II R&D Program Executive Office, Korea AerospaceResearch Institute, Daejeon 305-806, South Korea4Division of Aerospace Engineering, Korea Advanced Institute of Science and Technology,Daejeon 305-701, South Korea5Technical University of Denmark, Department of Wind Energy, Risø Campus,Rokilde 4000, Denmark
(Received 13 September 2013; accepted 11 April 2014; published online 25 April 2014)
Modern horizontal axis wind turbine blades are long, slender, and flexible
structures that can undergo considerable deformation, leading to blade failures
(e.g., blade-tower collision). For this reason, it is important to estimate blade
behaviors accurately when designing large-scale wind turbines. In this study, a
numerical analysis considering blade torsional degree of freedom, geometric
nonlinearity, and gravity was utilized to examine the effects of these factors on the
aeroelastic blade behavior of a large-scale horizontal axis wind turbine. The results
predicted that flapwise deflection is mainly affected by the torsional degree of
freedom, which causes the blade bending deflections to couple to torsional
deformation, thereby varying the aerodynamic loads through changes in the
effective angle of attack. Edgewise deflection and torsional deformation are
mostly influenced by the periodic gravitational force on the wind turbine blade.VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4873130]
I. INTRODUCTION
Wind farms now contain a great number of large-scale horizontal axis wind turbines. One
of the significant developments in the design of individual wind turbines is an increase in their
power capacity to minimize the cost of energy.1 Wind fluctuations strongly affect power output,
control systems, and maintenance of wind turbines, and especially their safety and stability.
Large wind turbine may give rise to loads that vary along the blade and change quickly in
response to varying wind conditions, such as turbulent and sheared flow conditions. For design
purposes, it is important to understand the distribution of turbulence energy among the poten-
tially significant periods or frequencies of fluctuation. Wind turbulence has a strong impact on
blade deformation. Heavy turbulence may generate large variations of aerodynamic loads acting
on the blade and thus may result in turbine failures and reduced life of the turbine.1,2
Moreover, wind velocity is proportional to the height from the ground due to the surface rough-
ness. With the continuously increasing blade length of wind turbines, wind loads according to
a)Author to whom correspondence should be addressed. Electronic mail: [email protected]. Tel.: þ82-42-350-3717. Fax:
þ82-42-350-3710.
1941-7012/2014/6(2)/023126/19/$30.00 VC 2014 AIP Publishing LLC6, 023126-1
JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY 6, 023126 (2014)
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blade position vary significantly, resulting in large unbalanced aerodynamic loads on the blades.
Thus, wind shear can also result in excessive blade deformations.
As mentioned above, the interaction between blade motions and wind speed variations
becomes more pronounced as wind turbines become larger.3 Fluid-solid coupling dynamics also
become more complex, and more serious coupling in wind turbines may cause blade damage
more easily. For instance, during the operation of wind turbines, a minimum clearance must be
maintained between the blade tips and the tower. For this reason, high blade stiffness is
required to avoid collisions between the blades and the tower; yet, in practice, the maximum
blade length is constrained by the required stiffness and stresses on blades. Therefore, to pre-
vent blade failures, simulations for accurately estimating the blade behavior of large-scale wind
turbines should be utilized in the design of flexible and slender wind turbine blades. To do this,
some important factors, such as torsional degree of freedom (DOF), geometric nonlinearity, and
gravity, must be considered in a numerical analysis. Many researchers in the wind industry and
research institutes use simulation codes to include the torsional DOF in estimates of the blade
deformations of their wind turbines4 (e.g., GH Bladed,5 HAWC2,6 BHawC,7 ADAMS,8
FLEX5,9 PHATAS,10 TURBU,11 etc.). Although these codes are relatively inexpensive compu-
tationally, some simulation codes (e.g., FAST12) do not include the torsional DOF of the blade;
thus, the predictions cannot consider the torsional deformations due to the aerodynamic pitching
moment. However, because the torsional deformation consequently affects the aeroelastic char-
acteristics as well as the aerodynamic characteristics through variations in the angle of attack,
an analysis including the torsional DOF should be utilized.13 In addition, the larger and more
flexible blade shape of the wind turbines introduces nonlinear blade behaviors.14 Numerous
approaches have been developed to cope with large deflection problems, such as elliptic integral
formulation, numerical integration with iterative shooting techniques, the incremental finite ele-
ment (FE) method, the incremental finite differences method, the method of weighted residual,
and the perturbation method.15,16 The European Commission-funded project UPWIND17–19
deals with nonlinear modeling of blades and the effects of including such geometric nonlinear-
ities. Also, the TURBU11 includes the effect of geometric nonlinearities.20 However, a fair
number of the available commercial programs for wind turbine design still use simplified linear
structural models, which cannot be applied to structures with considerable deformations.3,21–23
Furthermore, the blade behaviors are largely impacted by gravity, which induces excitation in
the rotating blade and becomes a more crucial vibration source as dimensions of the wind tur-
bine increases.24 For this reason, it is necessary to understand the various nonlinear interactions
including the effect of gravity, as well as the torsional DOF, on large-scale (larger than 5 MW)
wind turbine blades.
For fluid-structure interaction simulations, several different approaches for wind turbines
have been used. Until recently, the coupled computational fluid dynamics (CFD)-computational
structural dynamics (CSD) techniques have rarely been utilized for aeroelastic analysis of the
wind turbines.25,26 Baziles et al.25 and Yu and Kwon26 have developed the CFD-CSD methods
for estimating the static blade deflections and the aerodynamic results by the deformed blades.
These CFD-CSD computations have some limitations for use in an aeroelastic model, although
CFD approaches have ability to improve the prediction accuracy. A notable disadvantage of the
coupled CFD-CSD model is that it is computationally intensive and complex. For this reason,
blade element momentum (BEM)-CSD technique is the most widely used because of its sim-
plicity and low computational cost. Therefore, this study deals with the effects of torsional
DOF, geometric nonlinearity, and gravity on the aeroelastic behavior of a horizontal axis wind
turbine blade using the ABAQUS-BEM coupled method. The finite element software ABAQUS
is not a specific code for wind turbines, and has no built-in rotor-aerodynamics algorithms, but
allows users to link their own routines with aerodynamic modules.23 Therefore, in this study,
the ABAQUS/standard program is coupled with its aerodynamic solver based on a BEM
method, which takes in account the interaction of the factors of the torsional DOF, geometric
nonlinearity, and gravity. The results predict that flapwise deflections of a wind turbine blade
are predominantly influenced by the factor of the torsional DOF, while edgewise and torsional
deformations are mostly affected by the gravity.
023126-2 Jeong et al. J. Renewable Sustainable Energy 6, 023126 (2014)
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II. MODELING
A. Wind profiles under turbulent and sheared flow conditions
Wind condition is one of the most critical characteristics in wind turbine aerodynamics and
aeroelasticity. In fact, wind velocity varies in both time and space, and is determined by many
factors such as terrain and meteorological conditions.27,28 Because the wind condition, such as
turbulent flow, is a random parameter, measured wind data are usually considered using statisti-
cal methods.1 A turbulent flow environment includes critical features known to adversely affect
the aerodynamic and aeroelastic blade response and should be considered in the design phase
of wind turbine blades; however, the characteristics of the turbulent flow cannot be simulated
accurately by the normal turbulence models from the International Electro-Technical
Commission (IEC) 61400-1 standard.27 The National Renewable Energy Laboratory (NREL)
developed the TurbSim stochastic flow turbulence code to provide a numerical analysis of full-
field flow, including bursts of coherent turbulence associated with organized turbulent structures
in the flow.28 As mentioned earlier, the analysis code employs a statistical model to predict the
time series of three velocity components in a two-dimensional grid. The power spectra of the
three velocity components, and the spatial coherence, can be expressed in the frequency do-
main. Also, the time series is generated by an inverse Fourier transform (IFT).28 This study
utilizes the IEC Kaimal turbulence model for the numerical simulations, as it is capable of pro-
viding the most realistic flow conditions.29 Detailed descriptions of the Kaimal turbulence
model are reported in the NREL TurbSim User’s Guide technical report.28
Wind shear is a meteorological phenomenon in which wind velocity increases with the
increased height above the ground. The impact of height on the magnitude of the wind velocity
is related to surface roughness, and the wind profiles can be predicted using the following
Heckmann power equation:1,27
uðzÞ¼ uðz0Þz
z0
� �a
; (1)
where z is the height above the ground, z0 is the reference height for which wind speed u(z0) is
known, and a is the wind shear coefficient. In practice, a depends on a number of factors,
including the roughness of the surrounding landscape, height above the ground, time of day,
season, and locations.28 In the present research, a wind shear exponent of 0.2, which is the av-
erage value discussed in wind turbine design guideline, was used in all simulation cases.
B. Fluid-structure interaction analysis model
Blade element theory (BET) is an analytical method for predicting aerodynamic forces at
each blade section. Momentum theory denotes a control volume analysis of the blade loads
based on the conservation of the linear and angular momentum. The results of these two meth-
ods can be coupled with strip theory. The fundamental concept of the BEM method is to equal-
ize the linear and angular momentum changes of the masses flowing through the rotor plane
with the axial load and torque generated on the rotor blades. This equilibrium is accomplished
by considering the flow through annular strips of width and the aerodynamic loads on blade ele-
ments of the same width. Then, it is possible to compute the aerodynamic forces and pitching
moment for different conditions of wind speed, rotor speed, and collective pitch angle. The fac-
tors for calculating the induced velocity are defined as follows:13
a ¼ 4Ftiploss sin2/rCn
!þ 1
( )�1
; a0 ¼ 4Ftiploss sin / cos /rCt
� �� 1
� ��1
; (2)
where a and a0 denote the axial and tangential induction factors, respectively, and Cn and Ct
are the force coefficients in normal and tangential directions, respectively. The term r is the
blade solidity, which is defined as the ratio of blade area to rotor disk area (r¼Nb � c(r)/2pr,
023126-3 Jeong et al. J. Renewable Sustainable Energy 6, 023126 (2014)
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where Nb is the number of blades), and the term / is the angle between the rotor plane and the
resultant velocity, as shown in Fig. 1. The tip-loss factor developed by Prandtl was employed
to consider the impact of the discrete number of the blades, and the formulation can be
expressed as follows:
Ftiploss ¼2
pcos�1 exp �Nb
2
R� r
r sin /
� �� �; (3)
where the term R is the blade radius and r is an arbitrary position of the blade. Then, the effec-
tive angle of attack at the each blade section can be calculated as follows:
aeffective ¼ hflow � htotal ¼ tan�11� að ÞVwind cos /yaw
1þ a0ð ÞXr� Vwind sin /yaw
� �cos w
( )� htotal; (4)
where
htotal ¼ htwist þ hpitch þ hdeformed:
The term Vwind denotes the mean wind velocity; /yaw, the yaw angle; X, the rotor speed; W,
the azimuthal angle of the blade; htwist, the structural twist angle; hpitch, the collective pitch
angle; and hdeformed, the deformed angle caused by the torsional elastic motion.
By using a look-up table method of experimentally determined lift coefficient (Cl), drag
coefficient (Cd), and moment coefficient (Cm) data (as a function of the Reynolds number and
angle of attack), the aerodynamic forces in axial direction (Fu), tangential direction (Fv), normal
direction (Fw), and pitching moment (Mh) for each blade station can be estimated as follows:
Fu ¼ � Fgrav sin htotal cos w; (5)
Fv ¼1
2qCnV2
relcþ Fgrav sin htotal sin w ¼ 1
2qV2
relc
� �2
Cl cos /þ Cd sin /ð Þ þ Fgrav sin htotal sin w;
(6)
Fw ¼1
2qCtV
2relcþ Fgrav cos htotal sin w ¼ 1
2qV2
relc
� �2
Cl sin /� Cd cos /ð Þ � Fgrav cos htotal sin w;
(7)
Mh ¼1
2qCmV2
relc2; (8)
where the term q denotes the air density, Vrel is the resultant velocity, c is the chord length of
the blade, and Fgrav stands for the gravitational force (Fgrav¼m � g, where m is the mass of unit
FIG. 1. The local normal and tangential loads on a wind turbine blade.
023126-4 Jeong et al. J. Renewable Sustainable Energy 6, 023126 (2014)
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length, and g denotes the acceleration due to gravity). In order to apply the BEM method to the
horizontal axis wind turbine blades, some correction factors should be introduced into the simu-
lation process. The tip vortices generate multiple helical structures in the wake, which have a
large impact on the induced velocity distribution;30 but the BEM method cannot account for the
impact of vortices being shed from the blade tips into the wake.30 Thus, a tip-loss correction
model developed by Prandtl was applied to compensate for the deficiency of the induced veloc-
ity field. Yawed conditions can produce a skewed wake behind the rotor plane; therefore, the
BEM method requires correction to account for this skewed wake effect.20,31 Furthermore, the
aerodynamic forces for the BEM method demand correction to account for viscous effects. This
is accomplished by the Du-Selig dynamic stall model. Finally, the rotational augmentation cor-
rections for three-dimensional delayed stall were applied using AirfoilPrep,32 which uses the
Selig and Eggers methods to modify the lift and drag coefficients of the rotating blade.
In the present study, the BEM method is coupled with the ABAQUS/standard program to
examine the aeroelastic blade behaviors of large-scale wind turbines. State-of-art wind turbine
blades are generally not simple to model due to the distribution of anisotropic material proper-
ties and the complexity of their cross-section. Although these complex wind turbine blades can
be modeled accurately using complete finite element methods, they are too detailed for fluid-
structure interaction analysis. Thus, simplified beam model based on a series of equivalent
beam elements (the beam elements in ABAQUS that use linear and quadratic interpolation, i.e.,
element type B31) is used for aeroelastic simulation. Strong coupling, which means that the
aerodynamic loads (Fu, Fv, Fw, Mf, Mb, Mh) and structural displacements (u, v, w, f, b, h) are
exchanged at each time step, is employed for a fluid-structure interaction analysis as presented
in Fig. 2. The coupling schemes can be classified by the type and order of the interaction
method used for the aerodynamic solver (i.e., fluid) and the structural solver (i.e., structure).33
In this study, a first order implicit–explicit coupling scheme, which fundamentally consists of
the two steps, was employed.
As seen in Fig. 3, the phenomena by feeding back changes in structural geometry due to
elastic deformation of the blade is coupled with the aerodynamic solver to re-predict the aero-
dynamic loads. The discrete equation of motion at time iþ 1 for the horizontal axis wind tur-
bine blade is defined as follows:34
M½ � €uf giþ1 þ C½ � _uf giþ1 þ fintf giþ1 � fextf giþ1 ¼ rf giþ1 ¼ 0; (9)
where [M] and [C] denote the mass and damping matrices, respectively, and vector {r}iþ1 is
the residual, or out-of-balance force, which is zero when equilibrium is satisfied. By subtracting
from Eq. (9), the equivalent equation of motion at time i, an incremental form is obtained as
follows:
FIG. 2. The process of fluid-structure interaction analysis of wind turbine blades.
023126-5 Jeong et al. J. Renewable Sustainable Energy 6, 023126 (2014)
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M½ � D€uf gi þ C½ � D _uf gi þ Dfintf gi � Dfextf gi ¼ Drf gi ¼ 0: (10)
By a first-order linearization of the internal force and external force, we can obtain
Dfintf gi ¼@fint
@u
� i
Duf gi ¼ Kint½ �i Duf g; (11)
Dfextf gi ¼@fext
@u
� i
Duf gi ¼ Kext½ �i Duf g; (12)
where [Kint] denotes the consistent tangent stiffness and [Kext] stands for the load stiffness.
Inserting these linearized increments into Eq. (10) gives an equation where only the accelera-
tions and velocities at iþ 1 are unknown remains as follows:
M½ � D€uf gi þ C½ � D _uf gi þ Kint½ � � Kext½ �ð Þ Duf gi ¼ Drf gi: (13)
In a nonlinear context, [Kint] and [Kext] are in general functions of the displacement.
Equivalently, the gradients of the internal force and external force need not be linear.
Therefore, due to the linearization in Eqs. (11) and (12), the equilibrium equation at time iþ 1
is no longer exactly satisfied, giving a non-zero residual {r}iþ1. Details on these formulations
are well documented in the literature.34,35 In the present study, the discrete equation of motion,
as presented in Eq. (9), can be solved using the FE software ABAQUS/standard. The aeroelas-
tic model based on the ABAQUS-BEM coupled method is employed to predict the blade defor-
mations of the wind turbines at different operation conditions. The ABAQUS/standard program
is a powerful tool, especially for a complicated and flexible blade structure, because this tool
can offer several relevant modeling options.36 First, the slender and flexible wind turbine blade
is expected to experience the large deformations, contains structural couplings, and could have
a changing tangential stiffness matrix for nonlinear analysis;36 and second, an integrated Python
application programming interface (API) allows the user to completely manipulate ABAQUS
models and initiate analysis from the ABAQUS Python script command line. Thus, a Python
script can act as the bonding element between ABAQUS/standard program and any other code
or program, such as MATLAB.36,37
III. ANALYSIS MODEL: NREL 5 MW REFERENCE WIND TURBINE (RWT)
This study uses the NREL 5 MW RWT to investigate the aeroelastic behaviors through
fluid-structure interaction analysis. The geometric parameters and operational conditions are
presented in Table I.
The operational ranges can be divided into two sections: (1) the variable speed operational
range (from cut-in wind speed of 3 m/s to rated wind speed of 11.4 m/s) and (2) the pitch-
controlled operational range (from a rated wind speed of 11.4 m/s to a cut-out wind speed of
FIG. 3. Fluid-structure coupled computational process (implicit–explicit coupling scheme).
023126-6 Jeong et al. J. Renewable Sustainable Energy 6, 023126 (2014)
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25 m/s). Details on the structural and aerodynamic properties are well documented in the previ-
ous literature.38
A. Validations
1. Dynamic structural responses of the wind turbine blade
Table II presents the six lowest natural frequencies of the NREL 5 MW RWT blade at
zero rotational speed. Comparing the natural frequencies against the BModes39 and FAST40
codes, and showing good agreement for all modes, can be seen as a validation of the dynamic
structural behavior modeling capabilities of the beam approach using the ABAQUS/standard
program. BModes, which was developed by NREL, is a finite element code, and can provide
dynamically coupled modes for a beam model.39 Also, FAST code is an assumed-modes
approach code that uses only uncoupled modes for the flapwise and edgewise degrees of free-
dom. The natural frequencies are computed by conducting an eigenvalue analysis on the first-
order state matrix created from a linearization analysis in FAST code.40
B. Steady-state blade deflections under uniform flow conditions
The fluid-structure interaction analysis was performed for the NREL 5 MW RWT blade at
a rated wind speed under uniform flow condition. At the rated wind speed of 11.4 m/s, the cor-
responding rotor speed is 12.1 rpm, and the pitch control angle is set to zero degrees. For the
structural calculations, 50 finite elements were used along the span to model the structure of
the blade. The elastic axis was assumed to be located at the quarter-chord as presented by
NREL.38 Fig. 4 shows the blade tip deformation during the coupling iterations. The results pre-
dicted that the convergence was obtained in less than coupling iterations of five.
Fig. 5 shows the blade tip deflections under normal operating conditions for wind ranges
from cut-in to cut-out wind speed. These steady-state blade deformations are nondimensional-
ized by radius of the NREL 5 MW RWT blade. The rotor speed and collective pitch angle con-
trols are based on the data given by NREL.38 The present results are compared with those
obtained by FAST-AeroDyn for the blade bending deflections. FAST code is a modal-based
code which includes neither a torsion DOF of the blade nor non-linear geometric couplings, so
this prediction ignores torsional deformations due to the aerodynamic pitching moments that
TABLE I. Main characteristics of the NREL 5 MW reference wind turbine.36
Rated power 5 MW
Number of blades 3
Rotor/hub diameter 126 m/3 m
Cut-in/rated/cut-out wind speed 3/11.4/25 m/s
Cut-in/rated rotor speed 6.9 rpm/12.1 rpm
Airfoil section DU and NACA airfoils
Basic control Variable speed, collective pitch
TABLE II. Natural frequencies for the first 6 modes at zero rotation speed (unloaded case).
Mode number BModes (Hz) FAST (Hz) Present (Hz)
1 0.69 0.68 0.673
2 1.12 1.10 1.106
3 2.00 1.94 1.926
4 4.12 4.00 3.955
5 4.64 4.43 4.427
6 5.61 5.77 5.511
023126-7 Jeong et al. J. Renewable Sustainable Energy 6, 023126 (2014)
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occur with device actuations. The blade tip deflections at the rated wind speed are about
0.090�R and 0.0097�R in the flap and edge directions, which are very similar to the existing
results from FAST-AeroDyn.38 The overall tendency is well-predicted by the present method,
demonstrating its capability.
C. Results and Discussions
1. Effects of torsional degree of freedom, geometric nonlinearity, and gravity on
aeroelastic behavior under uniform flow conditions
a. Effect of torsional degree of freedom on blade deflections. To further investigate the effect
of blade torsional behavior on blade deformation, an ABAQUS-BEM coupled analysis includ-
ing torsional DOF was performed for the wind speed ranges from 3 m/s to 25 m/s. Fig. 6 shows
the present results of the tip deflections compared with the numerical results by CFD-CSD
coupled methods41 for the flapwise, edgewise bending deflections and torsional deformation.
The blade bending deflections are nondimensionalized by the radius of the blade. Some differ-
ences of flapwise and edgewise deflections at the rated wind speed were observed between the
present analytical method which includes the factor of the torsional DOF and the present ana-
lytical method that ignores such factors, with offsets of 18.37% and 15.38%, respectively. Also,
an elastic torsional deformation of �3� (toward the feather direction) at the rated wind speed of
11.4 m/s is shown during the normal operating conditions. For this reason, the present result,
which considers the torsional DOF, can lead to a noticeable under-prediction of blade tip dis-
placement as compared to the present results that ignores the torsional DOF. In other words, it
is clear that the torsional deformation considerably affects the aeroelastic behaviors of the
blade. Comparisons were also made with the present method and the CFD-CSD coupled
FIG. 4. Blade tip displacements during coupling iteration of the fluid-structure interaction at a rated wind speed of
11.4 m/s.
FIG. 5. Steady-state blade tip displacements under uniform flow condition.
023126-8 Jeong et al. J. Renewable Sustainable Energy 6, 023126 (2014)
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method,41 because both methods take into account the torsional DOF, and good agreement was
shown between the two methods of blade bending deflections. A similarity was observed in the
result of the torsional deformation, in which a negative peak at the rated wind speed was
shown.
The radial distributions of blade-bending deflections and torsional deformation at the rated
wind speed of 11.4 m/s are presented in Fig. 7. The present results also show good agreement
with the numerical results obtained using the CFD-CSD coupled method.41
To investigate the effect of blade deformations on the aerodynamic forces, the distributions
of the normal and tangential force obtained using the ABAQUS-BEM coupled method, called
deformed blade, and the BEM only computations, called undeformed blade, were compared
with those of the CFD-CSD coupled method41 in Fig. 8. These results demonstrate that blade
deformation leads to a significant reduction in both normal and tangential aerodynamic forces.
This variation of the aerodynamic loads is directly related to the reduced effective angle of
FIG. 6. Blade tip displacements under uniform flow conditions, considering torsional DOF.
FIG. 7. Spanwise distribution of blade deflections at the rated wind speed considering torsional DOF.
023126-9 Jeong et al. J. Renewable Sustainable Energy 6, 023126 (2014)
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attack resulting from the reduction of the torsional deformation, as shown in Fig. 7.
Comparisons were also made between the results from the present method and the CFD-CSD
coupled method,41 and good agreement was shown for the aerodynamic force in the normal and
tangential directions.
b. Effect of geometric nonlinearity on the blade deflections. To examine the effect of geometric
nonlinearity on the blade deformations, a geometrical nonlinear analysis using the ABAQUS-
BEM coupled method was made under normal operating conditions. The computed results of
the nondimensional blade tip deflections, compared with other results by FAST-AeroDyn38 for
the flapwise and edgewise deflections, are presented in Fig. 9. Some discrepancies of flapwise
and edgewise deflections at the rated wind speed of 11.4 m/s between the present nonlinear
analysis and linear analysis are observed, with offsets of 8.31% (6.08% in the case of simula-
tion including the torsional DOF) and 1.41% (2.61% in the case of simulation including the tor-
sional DOF), respectively. In the edgewise deflection, because the stiffness is relatively high
and resultant deflections are small, it is clear that the difference between the linear model and
the nonlinear model is negligible.
c. Gravity effect on the blade deflections. Fig. 10 shows the nondimensional tip deflections at
a rated wind speed of 11.4 m/s, which are driven only by the periodic gravitational loading.
Results excluding the gravity effect are also presented for comparison. The mean values of the
tip displacements caused by the gravity are nearly similar to the results obtained using the sim-
ulation that ignores the gravity effect. The edgewise and flapwise motions are dominated by
gravity, which is seen as the oscillations on the scale of 4.957 s (corresponding to the rotor
FIG. 8. Spanwise distribution of aerodynamic forces at the rated wind speed considering torsional DOF.
FIG. 9. Blade tip displacements under uniform flow conditions considering geometric nonlinearity.
023126-10 Jeong et al. J. Renewable Sustainable Energy 6, 023126 (2014)
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speed of 12.1 rpm). In addition, some differences of flapwise and edgewise deflections at the
rated wind speed were observed between the present analysis with or without the consideration
of gravity effect, with offsets of 6.58% (4.75% in the case of linear analysis model) and 4.32%
(4.25% in the case of linear analysis model), respectively. These magnitudes of unsteady varia-
tions are fairly large, indicating that the unsteadiness due to the gravitational loading is signifi-
cant. The variation of edgewise deflection is nearly identical to that induced by gravity only, as
shown in Fig. 10(b), indicating that the blade behavior in the edgewise direction is mostly
affected by gravitational loading.
2. Effects of torsional degree of freedom, geometric nonlinearity, and gravity on
aeroelastic behavior under combined flow conditions of turbulence and wind shear
To achieve maximum efficiency, modern blades are lightweight and flexible with large
diameters, and are therefore more susceptible to blade failure problems, such as blade–tower
collisions. In large-scale horizontal axis wind turbines, wind conditions of turbulence and wind
shear considerably alter the effective loads on the rotor blades and thus, the blade aeroelastic
behavior. Therefore, analysis for estimating the blade responses resulting from turbulent and
sheared flow conditions should be implemented.
In this study, the fluid-structure interaction analysis using the ABAQUS-BEM coupled
method was performed under the assumption of fixed values of rotor speed and no collective
pitch control under the combined turbulent and wind shear flow conditions. The aeroelastic
model is employed to analyze the blade response to wind speed oscillations. In order to gener-
ate the turbulent flow using TurbSim,28 the Kaimal turbulence model recommended by IEC
61400–3 (Ref. 42) was applied. The mean wind speed was set to 11.4 m/s (i.e., rated wind
speed), and the turbulence intensity of 10% (Kaimal turbulence model, Class A) was used with
41-by-41 vertical and lateral grid points. Total simulation time was 600 s, and a power law
exponent of 0.2 for the sheared flow was employed in all simulation cases. Thus, the combined
turbulent and sheared flow conditions (red solid line), as presented in Fig. 11, were used for the
simulations. In other words, Fig. 11 presents that the blade tip experiences the wind speed
when the blade rotates. Also, we assumed that the blade begins to rotate from azimuth angle of
zero, where the blade was positioned at vertical up.
To investigate the effects of torsional DOF, geometric nonlinearity, and gravity on the
blade aeroelastic behaviors, the fluid-structure interaction analysis including all such effects was
performed. Figs. 12–14 show the predicted flapwise tip displacements of the NREL 5 MW
RWT blade throughout the numerical simulations. The results demonstrate how the blade inter-
acts with wind speed variations. In other words, a change in the magnitude of wind velocity
has a considerable impact on the magnitude of blade deflections. These analysis results were
compared with the baseline results, which included the torsional DOF, geometric nonlinearity,
and gravity. The numerical analysis for investigating the effect of torsional DOF on the blade
deflection was conducted, and the blade responses are shown in Fig. 12. The results predict that
FIG. 10. Blade tip displacements at the rated wind speed, with consideration of gravitational loading.
023126-11 Jeong et al. J. Renewable Sustainable Energy 6, 023126 (2014)
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relatively low flapwise tip deflections are caused by the torsional deformations. This tendency
is also observed by the histogram plot. Analytical methods including the factor of the torsional
DOF can result in different predictions of blade behavior, since the variation of aerodynamic
loads resulted from the torsion deformations affects the blade-bending displacements. Similar to
the results shown in Fig. 6, analytical methods that consider the torsional DOF may cause a no-
ticeable under-prediction of flapwise tip deflections. A power spectral density (PSD) function is
the most common method of representing the responses in the frequency domain, and is
obtained by utilizing the fast Fourier transform (FFT). This PSD simply presents the frequency
contents of the time response and is an alternative way of specifying the time history of the
blade deflection. As seen in the figures, the dominant responses are observed in the vicinity of
FIG. 11. Pure turbulent flow condition (blue dashed line) and combined turbulent and wind shear flow conditions (red solid
line) at the blade tip for a total simulation time of 600 s.
FIG. 12. Blade flapwise tip deformations under combined turbulent with sheared flow conditions, considering the torsional
DOF.
023126-12 Jeong et al. J. Renewable Sustainable Energy 6, 023126 (2014)
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FIG. 13. Blade flapwise tip deformations under combined turbulent with sheared flow conditions, considering the geomet-
ric nonlinearity.
FIG. 14. Blade flapwise tip deformations under combined turbulent with sheared flow conditions, with consideration of
gravitational loading.
023126-13 Jeong et al. J. Renewable Sustainable Energy 6, 023126 (2014)
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the frequencies of 0.2 Hz (1P), 0.4 Hz (2P), and 0.6 Hz (3P). These oscillations result from var-
iations in both the gravitational force and the aerodynamic loads due to the sheared flow. The
results predict that the most dominant flapwise deflection is at a 1P frequency, since the rotation
frequency of the rotor is, at most, 0.2 Hz (1/rev). Also, notable differences in the response mag-
nitudes are observed due to the effect of torsional DOF.
Figs. 13 and 14 show the impacts of geometric nonlinearity and gravity on the blade aeroe-
lastic responses. Compared to the effect of torsional DOF, these factors have a relatively small
influence on flapwise deflections. As seen in the figures, a comparison with the results of a lin-
ear model indicates that suppression of certain high-order nonlinear models can lead to a no-
ticeable under-prediction of the blade deflections due to under-predicted aerodynamic loads. For
this case, it is seen that geometric nonlinearity is more pronounced when the blade is largely
deformed. The gravity effect arises from the rotation of the rotor blade, thus exciting blade at a
frequency corresponding to the rotational frequency of the wind turbine. Similar to the results
shown in Fig. 12, the dominant response in flapwise tip displacements is at the frequency of
1P. It is also shown that these oscillations are caused by variations of loads on the blade due to
the wind flow conditions and gravity. The root-mean-square deviation (RMSD) is a commonly
employed measure of the differences between values predicted by a numerical model and the
values in the baseline case. Thus, when measuring the average difference between two time se-
ries x1,i and x2,i, the formula is defined as follows:43
RMSD ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1
n
Xn
i¼1
x1;i � x2;ið Þ2s
; (14)
where n is the number of predictions. In the present study, the RMSD values were calculated
for each simulation case for comparison with the baseline result. The RMSD value of the effect
of the torsional DOF is 0.9545, whereas the RMSD values of the effects of the geometric nonli-
nearity and gravity are 0.3969 and 0.2523, respectively. In other words, the torsional DOF has
a stronger effect on flapwise blade deflection than the other factors. However, because substan-
tial differences between the blade responses are still observed, the factors of the geometric
nonlinearity and gravity cannot be ignored when attempting to accurately predict the blade
behavior of large-scale horizontal axis wind turbines.
Figs. 15–17 present the edgewise tip displacements of the NREL 5 MW RWT blade. It is
shown that the combined flow conditions of turbulence and wind shear are the primary factors
that lead to the considerable blade tip deformations in all directions. Similar to the numerical
results of the flapwise tip displacements, as presented in Figs. 12–14, the edgewise tip dis-
placements show almost irregular blade behavior. As seen in Figs. 15 and 16, small edgewise
displacements caused by torsional DOF and geometric nonlinearity are observed. However,
Fig. 17 shows that gravity most largely affects the edgewise deflections. This is because gravi-
tational force tends to dominate edgewise loading on the blade. The results in the frequency
domain predicted that the dominant responses are in the vicinity of the frequencies of 0.2 Hz
(1P), 0.4 Hz (2P), and 0.6 Hz (3P). Also, the dominant response in edgewise tip displacements
is shown to be at a 1P frequency, since the oscillations result from the variations of the flow
conditions and the gravitational force. The RMSD obtained by gravity is relatively high com-
pared to the RMSD obtained by the other factors. Therefore, a conclusion can be made that
edgewise blade motion is primarily driven by gravity, yet nearly unaffected by geometric
nonlinearity.
Figs. 18 and 19 show the torsional tip deformations of the wind turbine blade under com-
bined turbulent and sheared flow conditions. The results predict that the torsional tip deforma-
tions have almost periodic behavior. Similar to the edgewise tip displacements, as shown in
Figs. 15–17, gravitational force most greatly affects torsional motion. The results also demon-
strate that geometric nonlinearity fairly influences the torsional tip deformations. The RMSD
value observed for gravity is relatively high compared to the RMSD values for the other fac-
tors. This is because gravity has a large effect on torsional blade motion as well as on edgewise
023126-14 Jeong et al. J. Renewable Sustainable Energy 6, 023126 (2014)
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FIG. 16. Blade edgewise tip deformations under combined turbulent with sheared flow conditions, considering the geomet-
ric nonlinearity.
FIG. 15. Blade edgewise tip deformations under combined turbulent with sheared flow conditions, considering the torsional
DOF.
023126-15 Jeong et al. J. Renewable Sustainable Energy 6, 023126 (2014)
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FIG. 17. Blade edgewise tip deformations under combined turbulent with sheared flow conditions, with consideration of
gravitational loading.
FIG. 18. Blade torsional tip deformations under combined turbulent with sheared flow conditions, considering the geomet-
ric nonlinearity.
023126-16 Jeong et al. J. Renewable Sustainable Energy 6, 023126 (2014)
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motion. As a result of the introduction of gravity, the amplitudes of torsional deformations
become significantly higher than the deformations caused by geometric nonlinearity.
The main contribution of this study is the implementation of a fluid-structure interaction
analysis of a large-scale wind turbine blade that considers the effects of the torsional DOF, geo-
metric nonlinearity, and gravity. In each simulation of the given conditions, a fluid-structure
interaction analysis is performed on the NREL 5 MW reference wind turbine blade. The values
of the RMSD, as presented in Table III, are calculated by comparing the present results with
the baseline result, and to examine the interaction of each factor with the blade tip displace-
ments. As discussed above, a conclusion is drawn that the effect of the torsional DOF is the
main contributor to blade motion in the flapwise direction, while gravity most greatly affects
the blade displacements in the edgewise and torsional directions.
FIG. 19. Blade torsional tip deformations under combined turbulent with sheared flow conditions, with consideration of
gravitational loading.
TABLE III. RMSD values of the numerical predictions under combined flow conditions of turbulence (turbulent intensity
of 10%) and wind shear (power law exponent of 0.2).
Direction Considered effect Root-mean-square deviation
Flapwise tip displacements Torsional DOF 0.9548
Geometric nonlinearity 0.3969
Gravity 0.2523
Edgewise tip displacements Torsional DOF 0.1271
Geometric nonlinearity 0.0239
Gravity 0.2612
Torsional tip displacements Torsional DOF n/a
Geometric nonlinearity 0.1696
Gravity 0.3738
023126-17 Jeong et al. J. Renewable Sustainable Energy 6, 023126 (2014)
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IV. CONCLUSIONS
State-of-the-art horizontal axis wind turbines use extremely long and flexible blades that
can undergo large blade deformations. For this reason, accurately predicting blade behavior is
important to avoid blade failures, e.g., blade–tower collisions. In this study, the influences of
torsional DOF, geometric nonlinearity, and gravity in a fluid-structure interaction analysis on
the aeroelastic behavior of a large-scale wind turbine blade have been investigated under uni-
form flow conditions and under combined flow conditions of turbulence and wind shear. The
results predicted that the flapwise tip deformations are mostly influenced by torsional DOF,
which is mainly driven by coupling to torsional elastic deformations. Also, it is shown that
gravity is the greatest influence on edgewise and torsional tip deformations, whereas the other
factors have less impact on the blade deformations in these directions. However, because no-
ticeable differences are still observed as a result of geometric nonlinearity, as well as the fac-
tors of the torsional DOF and gravity, none of these factors can be ignored when attempting to
accurately predict the aeroelastic behavior of large-scale horizontal axis wind turbine blades.
Therefore, the results from this study suggest that torsional DOF, geometric nonlinearity, and
gravity should be considered in the fluid-structure interaction analysis for the design of flexible
and slender wind turbine blades.
ACKNOWLEDGMENTS
This research was supported by WCU (World Class University) program through the National
Research Foundation of Korea, funded by the Ministry of Education, Science and Technology
(R31-2008-000-10045-0). The authors are grateful for this support.
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