8th GRACM International Congress on Computational Mechanics
Volos, 12 July – 15 July 2015
WIND TURBINE BLADES PARAMETRIC DESIGN USING GRASSHOPPER®
1
2
3
4
Kyriakos G. Charalampous , Giorgos A. Strofylas , Georgios I. Mazanakis and Ioannis K. Nikolos
1,2,3,4
School of Production Engineering and Management
Technical University of Crete
Chania, GR 73100, Greece.
4
Contact author, e-mail: jnikolo@dpem.tuc.gr
Keywords: Wind Turbines, Parametric Blade Design, Internal Structure, NURBS.
Abstract. In this work a methodology for the parametric design of wind turbine blades is presented, developed in
Grasshopper®, a graphical algorithm editor tightly integrated into Rhinoceros® 3D Computer-Aided Design (CAD)
application. The presented methodology provides the ability to parametrically define the external blade geometry, as well as
the internal blade structure, including shear webs. The geometry definition procedure is parametric and a variety of wind
turbine blades can be produced. The blade’s outer surface definition is based on the use of 2D NURBS curves at successive
blade sections, constructed according to specified design parameters, while the resulting 3D surface is produced through
lofting. The internal structure can be constructed using different parameters in different blade regions, and specific surface
patches can be defined to this end. For each surface patch the blade thickness is parametrically defined, allowing for the
construction of blades with span-wise and chord-wise varying thickness. The developed algorithm eventually produces
compound solid blades, which can be further imported to mesh generation and analysis software through standard geometry
exchange protocols, for cooperation with Computational Fluid Dynamics (CFD) and Computational Structural Dynamics
(CSD) solvers. The blade design procedure, along with sample designs, generated computational meshes, and modal analysis
results, are presented in this paper to demonstrate the capabilities of the proposed methodology.
1 INTRODUCTION
Wind turbine blade design is one of the most important aspects of wind turbine technology [1, 2], targeting in
accomplishing the right balance between aerodynamic efficiency and structural reliability, especially in cases of large scale
wind turbines where the cost increases dramatically [3-5]. Thus, considerable efforts are continuously directed towards the
design of blades which can be accurately evaluated, utilizing the latest advances in all available computational tools, such as
CSD (Computational Structural Dynamics), CFD (Computational Fluid Dynamics) and various types of optimization
methods. To do so special attention should be given to the efficient and accurate geometry parameterization. Several
methodologies have been proposed so far for the design and analysis of wind turbine blades [6-10], the majority of which
relies on the definition of the blade’s three-dimensional surface from 2D airfoil profiles.
Various integrated software tools have been developed, either commercial or academic, for guiding the detailed design
and optimization of wind turbine blades. Such a software package for the optimum shape design and analysis of multi-MW
wind turbine blades was presented in [11]. Its main features include aerodynamic shape design and optimization, as well as
performance and pitch torque analysis for wind turbine blades. The accuracy of the performance analysis results have been
verified against the commercial package GH-Bladed [12], for a benchmark 5 MW blade of NREL. The designing concept of
GH-Bladed software is based on several structural and operational design parameters, such as blade diameter, rated speed,
design tip speed ratio etc., to construct a baseline blade, while the required chord lengths and twist angles of the sections along
the blade are computed according to the desirable operating conditions. A methodology based on the beam theory for the
analytical modeling of a small-scale vertical-axis wind turbine was presented in [13]; the geometric model concerns a straight
symmetrical blade, while the commercial software ANSYS [14] was utilized for its numerical modeling.
Pérez-Arribas and Trejo-Vargas used B-spline curves and surfaces to model the blades of horizontal-axis turbines; in their
approach the modeling of the 3D blade is based on a set of offsets of the 2D airfoil profiles, which are utilized for the
construction of the blade [15]. The design parameters correspond to geometrical entities, such as the skew and rake or coning
distribution. Attention is mainly directed towards the design of the leading and trailing edge areas of the blade, due to their
significant impact on the properties of the rotor. The final 3D surface is realized with the minimum possible control points, in
a way to accurately fit to the provided data points with a prescribed tolerance. An integrated environment, allowing for realtime observation of the numerical simulation under examination is provided by QBLADE [16]. The well-established software
XFOIL has been incorporated within QBLADE to facilitate the aerodynamic analysis of the produced blades. The software
provides a GUI to enable easy and accurate definition of the blade shapes, while the produced designs can be exported in
standard “STereoLithography” file formats.
Kyriakos G. Charalampous, Giorgos A. Strofylas, Georgios I. Mazanakis and Ioannis K. Nikolos
FOCUS6 [17], being a specialized software for the design of wind turbines, provides a variety of tools to determine
integrated blade designs. Its interactive nature allows direct feedback of the applied modifications to the design. The blade is
realized by the proper distribution of airfoil sections in the 3D space. Additionally, a database of various materials is provided,
along with their properties, to enable the material and thickness assignment at selected positions. The case study can be
exported both graphically and numerically, while it provides the ability to export meshes of thick shell elements with full
layup data, enabling in this way the analysis with FEM packages. NuMAD [18] is an interactive stand-alone, Matlab-based
[19] graphical pre-processor for the ANSYS FEM software, developed by Sandia’s team [20, 21]. It provides a user friendly
interface to set up the whole study of the blade design, including the definition of blades’ outer surface, shear web locations
and material assignment, along with a 3D viewer, enabling user’s interaction. It includes comprehensive databases of various
airfoil types and materials to allow for the efficient creation of blade models. Interaction between NuMAD and ANSYS is
achieved through the use of a sequence of ANSYS APDL commands, being the output of the software, utilized to create a
shell-type FE model in ANSYS.
A software tool named "T4T" (Tools for Turbomachinery), developed for the parametric design of turbomachinery and
wind turbine blades, was presented in [22, 23]. The proposed design procedure is object-oriented and parametric, providing
the ability to the user to define various types of blades. Developed in QT C++, and utilizing OpenCascade graphical and
computational libraries, T4T allows the user to design the outer surface either by specifying some physical parameters for
each blade section, or by directly interpolating a surface through a cloud of points. The computational procedure finally
produces compound solids, which can be further imported to mesh generation and analysis software.
Even though the use of a standard Computer-Aided Design (CAD) package to directly construct the model of a wind
turbine blade appears an obvious choice, it has the disadvantage of the limited access to the definitions of the various types
of curves and surfaces that are used by most of the commercial software to materialize the final model. The use of
Grasshopper® in this work overcomes this problem and provides the ability to construct parametric models for the geometric
definition of wind turbine blades, with increased capabilities in the definition and parameterization of the geometric entities
and functions, used to build the final model [24]. Moreover, the user takes advantage of all the infrastructure of the
Rhinoceros® software package, along with its available modeling tools [25]. The methodology presented in this work concerns
the parametric design of both the outer surface and the internal structure of wind turbine blades. Concerning the internal
structure definition, the blade is divided into regions in order to assign different laminate thicknesses and materials. This is
accomplished by defining specific surface patches, where the thickness of the laminated material can be parametrically
defined. Additionally, the parametric definition of shear webs geometry is also provided.
The paper is organized as follows: In section 2 and 3 the methodology of the parametric geometry definition is presented
for the blade’s outer surface and internal structure, respectively. In section 4 a sample blade design and analysis, based on real
data, is presented. Finally, section 5 contains some conclusions that emerged from this work.
2 BLADE SURFACE DEFINITION
In the proposed methodology, the definition of the outer blade surface relies on successive 2D airfoil profiles, representing
the cross-sections that form the blade; this feature was introduced to enable the use of standard airfoils, such as NACA and
DU (Delft University) ones, accelerating thus the design process and allowing for the easier definition of existing blade
designs. For each section’s definition, the 2D Cartesian coordinates are provided through appropriate text files in
dimensionless form, along with all the necessary design parameters being essential to the procedure, such as chord lengths
and stagger angles. Subsequently, the corresponding blade cross-sections are computed by a direct interpolation process
through a set of points, employing the method of curve fitting. The derived curves are distributed in perpendicular planes
along a stacking curve, which forms the pitch axis of the blade; their stacking points correspond to their centers of gravity.
This stacking curve is usually a straight line, however the ability to define various curves is provided, in order to produce prebend blades. The twist of the blade can be defined by applying the desirable twist angle for each section. By applying the
appropriate translation and rotation matrices the section curves are accordingly positioned in the 3D space (Fig. 1, left).
Two supplementary features, essential in cases where a large number of different airfoil types is used, are provided by the
developed methodology. The first one concerns the replication of sections’ coordinates that are used for multiple times along
the blade; thereby, the designer must provide only once the coordinates for a specific type of airfoil, along with the desirable
number of copies. Then, by applying the corresponding values of chord lengths and twist angles, the sections are converted
to a dimensional form and placed along the blade’s span. The second feature concerns the curve stacking order and is
complementary to the first one, allowing for the designation of each airfoil’s position along the stacking curve. It should be
noted that, for proper processing by the algorithm of the imported data, the value for the stacking order for each airfoil must
be in agreement with the corresponding values of their positions along the stacking curve. In this way, the preparation of the
airfoils’ parameters file is easier in cases where a particular type of airfoil is frequently used at non-consecutive positions.
Once the airfoils are properly positioned, the construction of the outer blade surface can be performed by using the
Kyriakos G. Charalampous, Giorgos A. Strofylas, Georgios I. Mazanakis and Ioannis K. Nikolos
constructed cross sections. Grasshopper® provides the ability to create surfaces through several ways; in the current work, the
surface is defined using the lofting procedure. To succeed this, all cross-sections are formed as single NURBS curves to avoid
discontinuity problems in the resulting surface. A sample design of a 3D blade surface is presented in Fig. 1 along with the
blade’s cross sections, utilized for the construction of its external surface.
Figure 1: The utilized cross sections (left) and the resulting 3D external surface of the blade (right).
3 INTERNAL STRUCTURE DEFINITION
Various ideas and methodologies have been proposed for the configuration of blade’s internal structure and the appropriate
selection of materials, allowing the blades to maintain high aerodynamic efficiency along with high structural integrity. The
definition approach for the internal structure proposed herein is general and representative of the current commercial blade
design trends. The procedure is fully parametric, allowing the user for constructing thick blades with shear webs.
3.1 Variable thickness assignment
Thickness assignment is perhaps the most difficult and complex step of the proposed methodology, due to the requirement
of different thicknesses in the chord-wise as well as in span-wise directions of the blade. To this end, a custom methodology
was developed to facilitate the procedure. The whole process begins by importing all the data needed to define the different
thicknesses, which correspond to pre-specified locations along the blade. More specifically, a number of regions where the
blade has to be split have to be specified first. Such regions are defined by selecting a pair of cutting planes for each one of
them, being perpendicular to the stacking curve. For each region the lower and upper cutting planes’ positions are defined as
percentages of blade’s length. Subsequently, the blade surface is sectioned by the aforementioned cutting planes and each
resulting region is manipulated separately for the assignment of different laminate thicknesses (Fig. 2).
For each blade region, the bounding cross-sections (lower and upper) have to be computed, along with their chord lines,
since they do not necessarily coincide with the initial cross sections, utilized for the construction of the outer surface of the
blade. An unlimited number of blade regions at arbitrary positions along the blade can be defined. Subsequently, for all
bounding sections, splitting points on the suction and pressure sides are defined in order to enable the assignment of different
thicknesses in the chord-wise direction. Note that the number of splitting points at the two bounding sections of each region
must be the same. The corresponding splitting points are defined as percentages of chords’ length; thereby, the chord length
for each boundary section of the blade region under consideration has to be computed. Subsequently, the normal vector to the
chord line is computed for each defined position. The intersection of that vector with the pressure and suction sides produces
Kyriakos G. Charalampous, Giorgos A. Strofylas, Georgios I. Mazanakis and Ioannis K. Nikolos
the corresponding splitting points, mapped on blade’s surface.
Figure 2: Blade sectioned in several regions (left), and an isolated region of the blade (right).
Figure 3: A blade region split in 7 surface patches (left); discrete points are extracted on the chord-wise bounding curves
of each patch (right-top); the moved points are interpolated to produce curves (right-middle), which are then connected
(right-bottom).
All of the splitting points are subsequently transferred to the , parametric space of the NURBS surface of the blade and
sorted appropriately into pairs (the first point at the lower section, and the second at the higher section of the blade region).
Kyriakos G. Charalampous, Giorgos A. Strofylas, Georgios I. Mazanakis and Ioannis K. Nikolos
Next, a single 2D curve is defined (in the parametric space) for each pair of points. Eventually, such curves are mapped on
the 3D surface of the blade, creating 3D NURBS curves that define each region of the blade. All of those curves define
separate surface patches (being their boundaries), which will provide later the ability to define different blade thickness
distributions in each one of them, as shown in Fig. 3.
Figure 4: Blade’s internal surface (left); the external and internal solid volumes of the blade (middle); the final hollow
blade (right).
At first, all surface patches’ wireframes (boundary curves) are computed; each wireframe consists of four edges, two in
the chord-wise direction and two in the span-wise direction. Subsequently, on the chord-wise edges of each wireframe a
predefined number of discrete points is produced, for which their , parametric coordinates on the NURBS surface are
computed. In this way the points can be mapped on the outer surface of the blade. The mapped points are used to define
interpolation curves on the NURBS surface. The resulting mapped curves are organized into groups so that every group
corresponds to a surface patch. The construction of a smoothly varying thickness in the span-wise direction of each patch is
based on the definition of the thickness in specific points on the two bounding curves, lying in the two chord-wise boundaries
of the patch. Discrete points on each one of the two curves are extracted first (Fig. 3 (right-top)). These points are then moved
inwards to the blade surface direction, in a distance equal to the blade thickness in the corresponding position. In this way a
varying thickness in the chord-wise and in the span-wise direction of each patch can be defined. The resulting moved points
can be then interpolated by a curve (Fig. 3 (right-middle)). As the adjacent patches may have different thicknesses, the
produced internal curves may not be continuous (Fig. 3 (right-middle)). For this reason, internal successive curves in the
chord-wise direction, produced for adjacent patches, are connected using linear segments (Fig. 3 (right-bottom)). Having such
internal curves defined in different positions in the span-wise direction, the internal surface of the blade can be easily
constructed by applying a lofting between all successive internal curves. The resulting internal surface is depicted in Fig. 4
(left).
The methodology presented above is effective and fast, as the generated curves can be easily converted to surfaces of high
quality and at the same time do not generate dysfunctions to the algorithm. Furthermore, through this procedure, a smoothly
varying thickness distribution along the blade span can be achieved, while different thicknesses in different chord-wise
positions can be easily defined. The main advantage however is its robustness; although the methodology utilizes the initially
produced external surface, the effectiveness of the methodology does not depend on the quality or the irregularity of this
surface. The external blade surface is used only for extracting points, which are then moved inwards to define the local
thickness of the blade. The external and internal surfaces are then transformed into solid volumes. A Boolean operation is then
used to subtract the internal volume from the external one and produce the hollow blade (Fig. 4).
3.2 Shear webs definition
To define the blade’s shear webs the algorithm provides the ability to assign smoothly varying thickness along the webs.
Kyriakos G. Charalampous, Giorgos A. Strofylas, Georgios I. Mazanakis and Ioannis K. Nikolos
For this purpose, each shear web is determined by a predefined number of web regions with different thicknesses. For each
web region, a starting and an ending plane section (normal to the stacking line) are defined, in a similar way to blade regions.
In addition, for each web region its position along sections’ chord is defined; a twist to the shear webs can be also provided.
Figure 5: A shear web with uniformly varying thickness (left) and a blade with two shear webs (right).
Figure 6: The graphical algorithm of the proposed methodology (top); the input and output structure of the developed
algorithm (bottom).
The chord-wise position of the web and its twist result from the specification of two pairs of intersection points, where the
first pair corresponds to the pressure side while the second pair corresponds to the suction side of the respective web region
bounding sections. The web’s thickness in each side of the blade is defined by a pair of points; each one’s position is defined
Kyriakos G. Charalampous, Giorgos A. Strofylas, Georgios I. Mazanakis and Ioannis K. Nikolos
as a percentage of the corresponding section's chord. Mapping curves on blade's surface (on suction and pressure sides of the
blade) are constructed by connecting the corresponding pairs of points being at the same side of the blade; these curves are
subsequently used as rail curves, which create the wireframes of the corresponding shear web. The lateral surface of the web
is produced as a sweep surface along the two wireframes. Finally, the surfaces which form the two main sides of the web are
created through patching the web’s lateral surface.
However, the webs may overlap the external surface of the blade. To address this problem the shear webs are slightly
compressed towards the interior of the blade. In this way the corresponding bounding curves of the web are positioned between
the external and internal surfaces of the blade, thereby ensuring the effective joining of the solid volumes of the webs with
the solid volume of the blade. Eventually, the webs are fused into the blade volume and a unified volume of the blade structure
is finally produced. A blade consisting of two shear webs is presented in Fig. 5, where the webs were defined using three web
regions with different thicknesses and twists.
All of Grasshopper® components (design tools), used for the construction of the algorithm, have been grouped together
into a cluster, which takes as inputs three input data files and produces the final solid blade (Fig. 6).
4 SAMPLE 3D BLADE DESIGN
4.1 Geometry description
The geometrical data for the frequently used NREL offshore 5-MW baseline wind turbine [26] were used to demonstrate
the corresponding capabilities of the proposed methodology. The geometric details of the blades used in this work are those
contained in the work of Martin [27]. The available data concern the cross-sections of the blade and are summarized in Table1.
All the airfoil types are included in the documentation of the NREL case in Table 1, where “Z-Radius” refers to the blade
airfoils’ locations along the span-wise direction, while “AeroTwist” refers to the aerodynamic twist angle, in degrees.
Section
Z-radius
(m)
Stacking
Curve
Percentage
AeroTwist
(Degrees)
Chord
Length
(m)
Airfoil Type
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
0
5.115
8.505
11.833
13.990
15.839
19.969
24.036
28.166
32.234
36.363
40.431
44.560
48.690
52.758
56.147
58.859
61.633
0
0.083
0.138
0.192
0.227
0.257
0.324
0.390
0.457
0.523
0.590
0.656
0.723
0.790
0.856
0.911
0.955
1
10.480
10.480
14.800
14.800
13.308
11.480
10.162
9.011
7.795
6.544
5.361
4.188
3.125
2.319
1.526
0.863
0.370
0.106
3.542
3.542
4.185
4.550
4.557
4.652
4.458
4.249
4.007
3.748
3.502
3.256
3.010
2.764
2.518
2.313
2.086
1.419
Cylinder1
Cylinder2
Cylinder3
Cylinder4
DU40_A17
DU35_A17
DU35_A17
DU30_A17
DU25_A17
DU25_A17
DU21_A17
DU21_A177
NACA64_A17
NACA64_A17
NACA64_A17
NACA64_A17
NACA64_A17
NACA64_A17
1st and 5th
patch
thickness
(m)
0.0435
0.0435
0.0541
0.0466
0.0456
0.0456
0.0456
0.0056
0.0456
0.0456
0.0276
0.0276
0.0276
0.0276
0.0276
0.0276
0.0276
0.0276
2nd and 4th
patch
thickness
(m)
0.0352
0.0352
0.0635
0.0677
0.1020
0.1020
0.0931
0.0837
0.0639
0.0522
0.0291
0.0291
0.0291
0.0291
0.0291
0.0291
0.0276
0.0276
3rd patch
thickness
(m)
0.0435
0.0435
0.0541
0.0466
0.0456
0.0456
0.0456
0.0054
0.0456
0.0456
0.0276
0.0276
0.0276
0.0276
0.0276
0.0276
0.0276
0.0276
Table 1: NREL blade properties, used for its geometry definition.
Although the utilized NREL blade is well documented regarding the aerodynamic characteristics, several details are
missing regarding the construction of the 3D blade surface. Information gaps exist concerning the coordinates of the 2D
airfoils and their stacking positions. Therefore, all non-dimensional 2D airfoil geometries and blade pitch axis locations were
obtained through other sources [21, 27, 28]. Combining all the available afore-mentioned resources, resulted in a blade
geometry which was constructed using the proposed methodology, as shown in Figure 7. Finally, laminate thicknesses were
applied on each of the five surface patches to produce a solid blade with a solid trailing edge, as described in Table 1, while
Kyriakos G. Charalampous, Giorgos A. Strofylas, Georgios I. Mazanakis and Ioannis K. Nikolos
the shear webs’ width was set to 0.0549 m.
Figure 7: NREL solid blade (left) and its cross-section with a solid tail and two shear webs (right).
4.2 Mesh generation and analysis
For demonstrating the effectiveness and versatility of the proposed blade definition methodology a complete analysis
procedure was implemented for the constructed geometry. As soon as the geometry is defined, a STEP file is extracted, which
is subsequently imported into a mesh generation software. For this particular work, the open source mesh generation software
GMSH [29] was used for the generation of the mesh of the internal structure. However, any mesh generation software, being
able to import geometric files in STEP format can be used, alternatively. GMSH is a three-dimensional finite element grid
generator software with build-in CAD engine and post-processor. It is designed to provide a fast, light, and user-friendly
meshing tool with parametric input and advanced visualization capabilities. One of the advantages of this software is the
ability to input and recognize different formats of geometric files, including STEP format, which allows the communication
with Rhinoceros® through a straightforward procedure. Moreover, it provides the ability of constructing unstructured and
structured meshes, using as a basis an initial surface mesh. In Figure 8 the generated unstructured volume mesh is presented.
Figure 8: The generated volume mesh, consisting of solid tetrahedral elements.
For the following modal analysis, CalculiX solver [30] was used; it is a free and open source Finite Element Analysis
application able to perform linear and non-linear calculations. Static, modal, dynamic, buckling and thermal simulations can
be performed. Furthermore, it has the ability to handle material and geometry non-linearity. A mesh converter was developed
to allow for the automatic import of mesh files from GMSH to CalculiX. The first six computed modes of the constructed
Kyriakos G. Charalampous, Giorgos A. Strofylas, Georgios I. Mazanakis and Ioannis K. Nikolos
blade, compared to the corresponding reference results of [31], are summarized in Table 2. Figure 9 presents the computed
first three deformation modes of the blade.
Mode
1
2
3
4
5
6
Frequency [Hz]
Present
Reference
computations
computations
[31]
0.7115
0.7066
1.0879
1.0188
1.9682
1.8175
3.0280
3.3403
3.8054
3.9493
5.8559
6.4682
Difference
[%]
0.70
6.78
8.29
-9.35
-3.64
-9.47
Description
1st flap-wise bending
1st edge-wise bending
2nd flap-wise bending
2nd edge-wise bending
3rd flap-wise bending
1st torsion
Table 2: Comparison between present and reference [31] predictions of the frequencies for the first 6 modes of the
simulated blade.
Figure 9: The three first modes of the blade model with a fixed root.
5 CONCLUSIONS
The aim of the work presented in this paper was to describe the development of an alternative methodology for the
parametric geometry definition of wind turbine blades, using the Grasshopper® graphical algorithm editor. The external blade
surface, as well as the internal blade structure, including shear webs, can be defined in a straightforward and automated
manner, by reading the corresponding parameters from external text files. 2D blade sections are used for the construction of
the 3D NURBS surface through a lofting procedure. The internal structure is generated by defining specific patches on the
external surface, enabling the construction of blades with span-wise and chord-wise varying thickness, fully controlled by the
user. The solid blades, produced by the described methodology, can be further imported to mesh generation and analysis
software through standard geometry exchange protocols. The developed computational procedure was tested in the
construction of a sample wind turbine blade, which was used for a modal analysis, utilizing an open-source FEM solver. The
application of the complete computational procedure, from geometry definition, through mesh generation, and finally the
structural analysis of the blade, demonstrated the robustness of the followed procedure, as well as its ability to produce detailed
and error-free geometrical descriptions of solid blades, which can be automatically re-shaped by simply changing their
parameters’ values, within pre-specified limits.
ACKNOWLEDGMENTS
This research has been co-financed by the European Union (European Social Fund - ESF) and Greek national funds through
the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) Research Funding Program: THALES: Reinforcement of the interdisciplinary and/or inter-institutional research and
innovation - Project: "Development of know-how on the aeroelastic analysis & design-optimization of wind turbines - WINDFSI". Investing in knowledge society through the European Social Fund.
Kyriakos G. Charalampous, Giorgos A. Strofylas, Georgios I. Mazanakis and Ioannis K. Nikolos
REFERENCES
[1] Singh, V.K., Thomas, T.T., Warudkar, V. (2013), “Structural Design of a Wind Turbine Blade: A Review”, International
Journal of ChemTech Research, Vol. 5(5), pp. 2443-2448.
[2] Gurit, (2013), Wind Turbine Blade Aerodynamics, Wind Energy Handbook, http://www.gurit.com/.
[3] Ackermann, T., Soder, L. (2002), “An overview of wind energy-status”, Renewable and Sustainable Energy Reviews,
Vol. 6, pp. 67–128.
[4] Ilkılıc C., Aydın, H., Behcet, R. (2011), “The current status of wind energy in Turkey and in the world”, Energy Policy,
Vol. 39, pp. 961–967.
[5] Leung, D.Y.C., Yang, Y. (2012), “Wind energy development and its environmental impact: A review”, Renewable and
Sustainable Energy Reviews, Vol. 16, pp. 1031– 1039.
[6] Henriques, J.C.C., Marques da Silva, F., Estanqueiro, A.I., Gato, L.M.C. (2009), “Design of a new urban wind turbine
airfoil using a pressure-load inverse method”, Renewable Energy, Vol. 34, pp. 2728–2734.
[7] Wang, Q., Chen, J.,Pang, X., Li, S., Guo, X. (2013), “A new direct design method for the medium thickness wind turbine
airfoil”, Journal of Fluids and Structures, Vol. 43, pp. 287–301.
[8] Zhang, W., Zou, Z., Ye, J. (2012), “Leading-edge redesign of a turbomachinery blade and its effect on aerodynamic
performance”, Applied Energy, Vol. 93, pp. 655–667.
[9] Kamoun, B. Afungchui, D., Abid, M. (2006), “The inverse design of the wind turbine blade sections by the singularities
method”, Renewable Energy, Vol. 31, pp. 2091–2107.
[10] Liu, X., Wang, L.,Tang, X. (2013), “Optimized linearization of chord and twist angle profiles for fixed-pitch fixed-speed
wind turbine blades”, Renewable Energy, Vol. 57, pp. 111-119.
[11] Kim, B., Kim, W., Lee, S., Bae, S., Lee, Y. (2013), “Development and verification of a performance based optimal design
software for wind turbine blades”, Renewable Energy, Vol. 54, pp. 166-172.
[12] Bossanyi, E.A. (2003), GH Bladed, theory manual, Doc. No. 282/BR/009.
[13] Hameed, M.S., Afaq, S.K. (2013), “Design and analysis of a straight bladed vertical axis wind turbine blade using
analytical and numerical techniques”, Ocean Engineering, Vol. 57, pp 248–255.
[14] ANSYS Inc. (2013), http://www.ansys.com, Canonsburg.
[15] Pérez-Arribas, F., Trejo-Vargas, I. (2012), “Computer-aided design of horizontal axis turbine blades”, Renewable
Energy, Vol. 44, pp 252-260.
[16] Marten, D., Wendler, J. (2013), Qblade Guidelines v0.6, http://qblade.npage.de/.
[17] WMC Knowledge Centre, 2013, FOCUS6 brochure, http://www.wmc.eu/focus6.php.
[18] Berg, J.C., Resor, B.R. (2012), Numerical Manufacturing and Design Tool (NuMAD v2.0) for Wind Turbine Blades:
User’s Guide, Sandia National Laboratories, SAND2012-7028.
[19] Mathworks, Matlab, https://www.mathworks.com/.
[20] Griffith, D.T., Ashwill, T.D. (2011), The Sandia 100-meter All-glass Baseline Wind Turbine Blade: SNL100-00, Sandia
National Laboratories, SAND2011-3779.
[21] Resor, B.R. (2013), Definition of a 5MW/61.5m wind turbine blade reference model, Sandia National Laboratories,
SAND2013-2569.
[22] Strofylas, G.A., Mazanakis, G.I., Nikolos, I.K. (2014), “Wind turbine blade structure parameterization using T4T”,
Proceedings of the ASME 2014 International Mechanical Engineering Congress & Exposition, IMECE2014, Nov. 14-20,
Montreal, Quebec, Canada, IMECE2014-39674.
[23] Strofylas, G.A., Nikolos, I.K. (2013), “Wind turbine blade design using T4T”, Proceedings of the 10th HSTAM
International Congress on Mechanics, Chania, Crete, Greece.
[24] Robert McNeel & Associates, GrasshopperTM, http://www.grasshopper3d.com.
[25] Robert McNeel & Associates, RhinocerosTM, http://www.rhino3d.com.
[26] Jonkman, J., Butterfield, S., Musial, W., Scott, G. (2009), Definition of a 5-MW Reference Wind Turbine for Offshore
System Development, National Renewable Energy Laboratory, NREL/TP-500-38060.
[27] Martin, H.R. (2011), Development of a scale model wind turbine for testing of offshore floating wind turbine systems,
M.Sc Thesis, The Graduate School, The University of Maine, Orono.
[28] NREL's National Wind Technology Center forum, https://wind.nrel.gov/forum/wind/viewtopic.php?f=2&t=440.
[29] Gezaine, C., Remacle, J.-F. (2014), GMSH: A finite element mesh generator with built-in pre- and post-processing
facilities, Version 2.8.4, http://geuz.org/gmsh/.
[30] Dhondt, G. (2014), CalculiX CrunchiX User’s Manual, version 2.7, http://www.dhondt.de/ccx_2.7.pdf.
[31] Laco, L.I. (2012), Structural response and dynamics of fluid structure-control interaction in wind turbine blades, Ph.D.
Thesis, Michigan Technological University.