
Research Article


Modal Analysis for Blade of Horizontal Axis Wind Turbine 

Nitin Tenguria,
N.D. Mittal
and
Siraj Ahmed



ABSTRACT

The blade of a wind turbine is very important component of the rotor. Now days the use of wind turbine generator has rapidly spread as the clean energy recourse and its size is also getting larger. Because of the difficulty of the maintenance of such large wind turbine blade the model analysis becomes important. In this work, the model analysis is done on a blade of length 38.95 m which is designed for V821.65MW horizontal axis wind turbine (supplied by Vestas). The airfoil taken for the blade is NACA 63_{4}221 which is same from root to tip. For doing this model analysis five shapes of spar are used. This analysis is done on finite element analysis software ANSYS 12.0. This approach gives satisfactory results and can be used for vibration analysis of turbo machinery blades and helicopter rotor blades. Natural frequency is lower in the case single web spar.





Received: May 06, 2011;
Accepted: June 07, 2011;
Published: September 08, 2011


INTRODUCTION
The design of a wind turbine blade involves many considerations such as strength,
stability, cost and vibration. Reduction in vibration is a very important measure
for a successful design of blade structure. It may promote other important design
goals, such as low cost and high stability level. A good design attitude for
reducing vibration is to divide the natural frequencies of the structure from
the harmonics of rotor speed. This would avoid resonance where large amplitudes
of vibration could severely damage the structure (Tenguria
et al., 2011). According to Maalawi and Negm
(2002), with the growth of wind energy, the problem of destruction of blade
caused by the vibration has attracted widespread attention and concern in the
engineering field. Hence the designing and modal analysis of the blade has become
a key process.
Pritchard and Adelman (1990) described methods for
reducing vibration in helicopter rotor blades by determining the optimal sizes
and locations of tuning masses through formal mathematical optimization techniques.
He developed an optimization procedure that employs the tuning masses and corresponding
locations as design variables that are systematically changed to achieve low
values of shear without a large mass penalty. Sabuncu and
Thomas (1992) investigated free vibration characteristics of rotating, shrouded,
pretwisted aerofoil crosssection blade packets using finite element model.
One end of the blade is supposed to be fixed at the periphery of a disk rotating
about its centre, whereas the other end of the blade is connected by a curved
shroud. He neglected shear deformation and rotary inertia effects and derived
the expressions for kinetic and strain energies of a pretwisted blade packet
subjected to centrifugal force. Bielawa (1992) has presented
a review of several approximate methods such as Myklestad method, Galerkin method,
RayleighRitz method, Finite Element Method (FEM), etc., for modal analysis.
Baumgart (2002) derived a mathematical model for an
elastic wind turbine blade which is mounted on a rigid test stand and compared
it with experimental results. Despite the few degrees of freedom and uncertainties
in the model parameters, the mathematical model approximates the measured blade
dynamics. Maalawi and Negm (2002) presented an optimization
model for the design of a typical blade structure of horizontalaxis wind turbine.
The crosssectional area, radius of gyration and length of each segment are
chosen as optimization variables. The main spar is represented by thinwalled
tubular beam composed of uniform segments each of which has different crosssectional
properties and length.
Tenguria et al. (2010) generated a computer
program for designing a blade for 5 KW horizontal axis wind turbine using blade
element momentum theory. He used different tip speed ratio for evaluating the
power coefficient. Jain and Mittal (2008) has studied
the distribution of stress and deflection in rectangular isotropic, orthotropic
and laminated composite plate with central circular hole under transverse static
loading using finite element methods. Eker et al.
(2006) investigated the use of composite material in wind turbine blade
for making them more resistant to impact. His study was based on theories of
wind technology and material science.
Friedman and Kosmatka (1993) developed the stiffness,
mass and consistent force matrices for a simple twonode Timoshenko beam element
based upon Hamilton's principle. The presented numerical shows that the current
element exactly predicts the displacement of a short beam subjected to complex
distributed loadings using only one element and the current element predicts
shear, moment resultants and natural frequencies better than existing Timoshenko
beam elements. Farghaly (1994) investigated the natural
frequencies and the critical buckling load coefficients for multispan beam
systems consisting of elastically supported uniform Timoshenko beams which may
be loaded with end as well as intermediate masses. The study of Farghaly
and Gadelrab (1995) is concerned with an additional expected gain in natural
frequencies for a onespan beam with a stepwise variable cross section made
of unidirectional fibre composite materials of different fibre volume fraction.
The study of Corn et al. (1997) is concerned
with the dynamic behaviour of Timoshenko beams. He proposed a new method in
a simple and systematic manner for constructing a twonode finite element based
on Guyan condensation that leads to the results of classical formulations. Rao
and Gupta (2001) have derived the stiffness and mass matrices of a rotating
twisted and tapered beam element. He assumed angle of twist, breadth and depth
to vary linearly along the length of beam and considered the effects of shear
deformation and rotary inertia in deriving the elemental matrices. Kisa
(2004) has investigated the effects of cracks on the dynamical characteristics
of a cantilever composite beam, made of graphite fiberreinforced polyamide.
The finite element and the component mode synthesis methods are used to model
the problem.
Vardar and Unal (2006) emphasized the use of individual
wind turbine towards meeting the electricity demands of a plant. He revealed
the electrical energy demand of the plant and then he used mathematical equations
for checking the selected wind turbine for electricity demand. Xu
et al. (2006) obtained the loss of power supply probability by simulation,
which is the index of power reliability. He found the Paretooptimal solutions
by using the elitist nondominated sorting GA (NSGAII) and he validated it
by solving the multiobjective problem with tangency method, which also belongs
to the constraint method.
Izli et al. (2007) used a computer program to
find fourteen different Reynold numbers, four different NACA profiles and lifting
and drifting coefficients. He calculated appropriate sliding rates of wind turbine
blade profile for each angle of attack by those values. Hsu
(2007) has formulated the dynamic problem of the wind turbine generators
by employing the differential quadrature method. He used the EulerBernoulli
beam model to characterize wind turbine generator blade. The study of Kallesoe
(2007) extends partial differential equations of blade motion, by including
the effects of gravity, pitch action and varying rotor speed. He also derived
equations for describing the pitch action and rotor speeds. Bana
Sharifian et al. (2008) studied maximum power control of wind turbine
and induction generator which are connected with two back to back voltage source
converters to grid. Wang et al. (2008) developed
a mathematical model using both beam finite element and thinwalled structure
theory to predict the natural frequency and blade behaviour of a horizontal
axis wind turbine under constant wind speed and turbulence condition.
Babainejad and Keypour (2010) have developed a model
of the variable speed wind turbine with doubly fed induction generator as a
compact block in the simulation tool i.e., MATLAB/SIMULINK. The parameters which
he has been considered are rotor resistance, stator resistance, leakage stator,
rotor inductance and mutual inductance. Vertical axis wind turbine is also attracting
many researchers. Beri and Yao (2011) showed the effect
of camber airfoil on self starting of vertical axis wind turbine at low Reynolds
number. He used moving mesh technique to investigate two dimensional unsteady
flows around turbine.
In the present study first of all, a computer program is developed on the basis
of Glauert's optimal rotor theory for getting the dimensions of 38.95 m wind
turbine blade. After this model analysis of blade is done with the help of ANSYS
12.0 using different shape of spars. EGlass/Epoxy prepreg material is chosen
as material and the properties are taken from the work of Brondsted
et al. (2005). The objective of this study is getting natural frequency
of wind turbine blade with different shapes of spar.
COMPUTATIONAL METHODS The Finite Element Method (FEM) is very useful and has traditionally been used in the development of wind turbine blades for investigating the global behavior in terms of Eigen frequencies, tip deflections and global stress/strain levels, respectively. The FEsimulation usually predicts the global stiffness and stresses with a highquality accuracy. Local deformations and stresses are often more difficult to predict and little work has been published in this area. The reason is that the highly localized deformations and stresses can be nonlinear, while the global response appears linear for relatively small deflections. Another reason is that a relatively simple shell model can be used for representing the global behavior, while a computationally more expensive 3Dsolid model may be necessary to predict this localized behavior. Even with a highly detailed 3D solid model it would rarely be possible to predict deformations or stresses accurately without calibration of the FEmodel. This calibration is required due to large manufacturing tolerances. Features such as box girder corners and adhesive joints often vary from specifications. Geometric imperfections are often seen and can cause unexpected behavior, especially relating to the strength predictions but also the local deformations can be affected. A big advantage of using FEM is that, once the model is set up and calibrated, complex load cases representing actual wind conditions can be analyzed. Only idealized loads can be imposed in a fullscale test and in this study the critical flapwise load case is evaluated. The 8noded shell 63 element type with 6 degree of freedom has been used with an element thickness provided 30 mm. TWIST, CHORD AND THICKNESS DISTRIBUTION
The twist of a wind turbine blade is defined in terms of the chord line. It
is a synonym for the pitch angle. However, the twist defines the pitch settings
at each station along the blade according to the local flow conditions. The
pitch angle (β) is large near the root (where local speeds are low) and
small at the tip (where local speeds are high). The wind angle varies along
the blade due to the increase in blade speed with increase in radial distance.
Hence to maintain optimum angle of attack of the blade section to the wind,
it must be twisted along its length. According to Hau (2006),
the twist distribution is maintained such that the lift coefficient will be
maximum at every station Fig. 2 is showing the twist distribution
of the designed blade which is varying exponentionally from root to tip. The
maximum value of twist is at root (38.12°) and the minimum value occurs
at tip (3.6°). Chord direction is perpendicular to the span direction and
lies in the plane extending through the leading edge and the trailing edge.
The behavior of the curves for chord and thickness distribution is same both
are increasing from root to shoulder than reducing exponentionally. The maximum
value of the chord at the shoulder is 6.24 m and at the tip is 1.36 m. As we
can see from Fig. 1 shoulder is the point where chord is maximum
and it is minimum at the tip of the blade. Stresses are maximum at the blade
root so that the blade root is the thickest portion of the blade.

Fig. 1: 
Chord distribution 

Fig. 2: 
Twist distribution 

Fig. 3: 
Thickness distribution 
The variation of thickness is shown in Fig. 3, which is calculated
in terms of percentage of length of chord and it is being calculated at all
stations of the designed blade. The chord is calculated on the concept used
by Ryu and Kim (2004).
Blade properties: The aerodynamic profiles of wind turbine blades have
vital control on aerodynamic efficiency of wind turbine. In this work, the length
of the blade is 38.95 m and the analysis is done for five shapes of spar. In
the study of Kooij (2003) it is given that the location
of the main spar with the location of the stiffening ribs will have the biggest
effect on the bending modes of the blade. In this study, the model of blade
is made of shell element as shown in Fig. 4. According to
Guidelines GDWT (2002), the blade is to be twisted around
the elastic axis. The position of elastic centre can be varied by modifying
the location of spars and its shape. The geometry of blade is modeled in ANSYS
to obtain the required properties of the blade and position of spars. The blade
is divided into 19 sections. Twist of the blade decides the value of aerodynamic
loads and also the direction in which the blade will vibrate. In this work the
spar is also twisted according to airfoil. The blade with twisted spars is shown
in Fig. 5 to 9.The boundary condition taken
is this analysis is same as cantilever beam.
Natural frequency: Figure 10 shows the first six
lowest natural frequencies obtained from ANSYS for the blade with different
shapes of spar. As we can observe from the Fig. 10, natural
frequency for the blade with single web spar is less than other shapes of spar.

Fig. 5: 
Blade with single web spar 

Fig. 6: 
Blade with double web spar 

Fig. 7: 
Blade with triangular spar 
 Fig. 8: 
Blade with cross shape spar 

Fig. 9: 
Blade with square shape spar 

Fig. 10: 
Natural frequency 
The behavior of the graph for all spar shape is same. The natural frequency
is increasing from mode 1 to 6. Natural frequency of single web spar for mode
1 is 0.2814 and for mode 6 is 4.3091.
CONCLUSION In this study, a blade is designed for horizontal axis wind turbine by using Glauert's optimal rotor theory. For designing blade the lift coefficient is taken constant throughout the blade. Reduction of vibration is a good measure for a successful design of blade structure. It may foster other important design goals, such as low cost and high stability level. A good design philosophy for reducing vibration is to separate the natural frequencies of the structure from harmonics of rotor speed. This would avoid resonance where large amplitudes of vibration could severely damage the structure. In this study, model analysis is performed on a typical pretwisted wind turbine blade with a nonuniform cross section and the cantilever boundary condition at the root. Figure 10 show that the weight of blade increases natural frequencies increases.

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