wind turbine blades parametric design using …8gracm.mie.uth.gr/papers/session d2-c3/k....

8th GRACM International Congress on Computational Mechanics Volos, 12 July – 15 July 2015

WIND TURBINE BLADES PARAMETRIC DESIGN USING GRASSHOPPER®

Kyriakos G. Charalampous1, Giorgos A. Strofylas

2, Georgios I. Mazanakis

3 and Ioannis K. Nikolos

4

1,2,3,4 School of Production Engineering and Management Technical University of Crete Chania, GR 73100, Greece.

4 Contact author, e-mail: [email protected]

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 real-time 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 pre-bend 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


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


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).


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.


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


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 1st and 5th patch

thickness (m)

2nd and 4th patch

thickness (m)

3rd patch thickness

(m)

1 0 0 10.480 3.542 Cylinder1 0.0435 0.0352 0.04352 5.115 0.083 10.480 3.542 Cylinder2 0.0435 0.0352 0.04353 8.505 0.138 14.800 4.185 Cylinder3 0.0541 0.0635 0.05414 11.833 0.192 14.800 4.550 Cylinder4 0.0466 0.0677 0.04665 13.990 0.227 13.308 4.557 DU40_A17 0.0456 0.1020 0.04566 15.839 0.257 11.480 4.652 DU35_A17 0.0456 0.1020 0.04567 19.969 0.324 10.162 4.458 DU35_A17 0.0456 0.0931 0.04568 24.036 0.390 9.011 4.249 DU30_A17 0.0056 0.0837 0.00549 28.166 0.457 7.795 4.007 DU25_A17 0.0456 0.0639 0.045610 32.234 0.523 6.544 3.748 DU25_A17 0.0456 0.0522 0.045611 36.363 0.590 5.361 3.502 DU21_A17 0.0276 0.0291 0.027612 40.431 0.656 4.188 3.256 DU21_A177 0.0276 0.0291 0.027613 44.560 0.723 3.125 3.010 NACA64_A17 0.0276 0.0291 0.027614 48.690 0.790 2.319 2.764 NACA64_A17 0.0276 0.0291 0.027615 52.758 0.856 1.526 2.518 NACA64_A17 0.0276 0.0291 0.027616 56.147 0.911 0.863 2.313 NACA64_A17 0.0276 0.0291 0.027617 58.859 0.955 0.370 2.086 NACA64_A17 0.0276 0.0276 0.027618 61.633 1 0.106 1.419 NACA64_A17 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


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


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

Frequency [Hz] Difference [%]

Description Present

computations Reference

computations [31]

1 0.7115 0.7066 0.70 1st flap-wise bending 2 1.0879 1.0188 6.78 1st edge-wise bending 3 1.9682 1.8175 8.29 2nd flap-wise bending 4 3.0280 3.3403 -9.35 2nd edge-wise bending 5 3.8054 3.9493 -3.64 3rd flap-wise bending 6 5.8559 6.4682 -9.47 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 - WIND-FSI". Investing in knowledge society through the European Social Fund.


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