Development and validation of tools for the structural design of wind turbine blades

In the beginning of his doctoral studies, the author had the chance to participate in the design of a 10 kW wind turbine. This turbine, was designed at ÉTS and manufactured in the course of a project funded by the Natural Sciences and Engineering Research Council of Canada’s Wind Energy Strategic Network (NSERC/WESNet). In this project, the author was involved in the structural design and validation of the blades. This wind turbine was designed and manufactured over a 15-month period, between January 2011 and March 2012 and was installed at the Wind Energy Institute of Canada (WEICan) on Prince Edward Island in June 2012.

As all the characteristics of this blade were available and as five blades were available for further testing, this blade design is used throughout this thesis as an example for the numerical and experimental work.

Wind turbine characteristics

This turbine is a pitch regulated variable speed wind turbine equipped with a direct drive synchronous generator designed at the University of New Brunswick (Canada). The rotor diameter is 8.08 m and the turbine reaches its nominal electric power of 10 kW at a wind speed of 9.5 m/s and a rotor speed of 185 rpm. For wind speeds below this value, the blade pitch angle is fixed and the rotor speed is adjusted to get the maximum power output. For winds above the nominal speed, the pitch control system is activated to maintain the rotor speed as close as possible to 185 rpm and consequently limit the power output to 10 kW. No yaw control system is needed as the rotor uses a downwind configuration and the nacelle yaw motion is unconstrained. The rotor therefore auto aligns itself when the wind direction changes.

Blade aerodynamic design 

The blade aerodynamic design was done by Jon Sumner, Ph.D. student at ÉTS. The blade uses airfoils of the Delft University of Technology family (Timmer and van Rooij, 2003) and was designed using blade element momentum (BEM) theory. As the aerodynamic design has to consider both aerodynamic and structural considerations, in the early stages of the aerodynamic design, conservative characteristic loads were used to verify that the current design met the structural requirements.

Blade loads computation 

Once the aerodynamic design was fixed, to determine the blade design loads, the turbine was analyzed using the aeroelasticity code FAST (Jonkman and Buhl Jr., 2005). This software models the entire wind turbine as an assembly of rigid and flexible bodies. In our analysis, all parts were considered rigid and the only degrees of freedom that were taken into account were the nacelle yaw motion and the variable rotor speed.

As the wind turbine is a free yaw downwind machine, the only control strategies to model were the variable rotor speed and the blade pitch control mechanism. The variable rotor speed control was modelled by specifying the torque vs. rotational speed curve of the generator as supplied by the designer. The pitch control system uses a proportionalintegral controler. The control systems was modelled with Simulink using the FAST’s Simulink interface by Tommy Gagnon, a master’s degree student at ÉTS.

All the relevant ultimate load cases of the aeroelastic method defined in the International Electrotechnical Commission (IEC) standard on design of small wind turbines (International Electrotechnical Commission, 2005) were evaluated using FAST. These load cases include normal power production, power production with control system fault, shut down, idling and parked wind turbine for different wind conditions.

The fatigue load cases were treated differently. In addition to the aeroelastic method, the IEC standard presents a simplified method to evaluate conservative load cases. The simplified fatigue load case is based on the load range of a wind turbine that operates between 0.5 and 1.5 times the design rotor speed and 0.5 and 1.5 times the rotor aerodynamic torque. The simplified method also includes the possibility to analyze the fatigue load case as a static load case using a safety factor of 10 on static material strengths. The fatigue load case used is based on this procedure. The nominal operation condition was modelled with FAST to get the aerodynamic loads and the gravitational and inertial loads were applied directly in the finite element model.

This analysis of all load cases with FAST allowed the identification, in addition to the fatigue load case, of three critical load cases to use for the blade structural design: maximum root axial force, maximum root edgewise bending moment and maximum root flapwise bending moment. The maximum root axial force and edgewise bending moment occur when the wind turbine in normal operation is submitted to the normal turbulence model with a wind speed of 25 m/s. The maximum root flapwise bending moment happens when the wind turbine in normal operation faces the extreme operating gust at nominal wind speed. During this situation, wind speed increases suddenly from 9.5 m/s to 14 m/s and then reduces to 9.5 m/s. This causes an acceleration of the rotor speed that causes a rapid nacelle yaw movement generating high out-of-plane gyroscopic forces. These forces are in the opposite direction of the aerodynamics forces so that the blade’s upper surface is in tension and the lower surface is in compression.

Table des matières

INTRODUCTION
0.1 Context : wind turbine blades
0.2 Structural design process of a wind turbine blade
0.3 Two contexts of blade structural analysis
0.3.1 Structural dimensioning and validation of the blade
0.3.2 Computation of blade cross-sectional properties for aeroelastic analysis
0.4 Two types of structural analysis models
0.4.1 Beam models
0.4.2 3D shell finite element models
0.4.3 Discussion
0.5 Thesis objectives
0.6 Thesis plan
CHAPTER 1 WESNET BLADE AND TEST METHODOLOGY
1.1 Introduction
1.2 Wind turbine characteristics
1.3 Blade aerodynamic design
1.4 Blade loads computation
1.5 Blade structural design
1.6 Blade manufacturing
1.7 Tests methodology
1.7.1 Modal analysis
1.7.2 Design load test
1.7.3 Cross-sectional characterization test
1.7.4 Destructive test
CHAPTER 2 LOADS ON A WIND TURBINE BLADE AND THEIR TRANSFER FROM AN AEROELASTIC SIMULATION TO A 3D FINITE ELEMENT MODEL
2.1 Introduction
2.2 Loads on a wind turbine blade and methodology
2.3 Distribution of loads on the blade and blade root loads
2.3.1 Aerodynamic loads
2.3.2 Gravitational loads
2.3.3 Inertial loads due to rotor rotation
2.3.4 Inertial loads due to rotor acceleration
2.3.5 Inertial loads due to nacelle rotation
2.3.6 Inertial loads due to nacelle acceleration
2.3.7 Inertial loads due to gyroscopic effect
2.4 Application of loads in a three-dimensional finite element model
2.4.1 Aerodynamic loads
2.4.2 Gravitational loads
2.4.3 Inertial loads due to rotor speed and acceleration
2.4.4 Inertial loads due to nacelle speed and acceleration
2.4.5 Inertial loads due to gyroscopic effects
2.5 Application on the WESNet 10 kW wind turbine
2.6 Conclusion
CHAPTER 3 WIND TURBINE BLADE STRUCTURAL MODELS
3.1 Introduction
3.2 Generalities about beam cross-sectional properties
3.2.1 Cross-sectional stiffness matrix Ks
3.2.2 Coordinate system transformation
3.2.3 Shear centre
3.2.4 Elastic centre
3.2.5 Principal axes of bending
3.3 Model 1: Simple model
3.4 Model 2: Classical strength of materials model
3.4.1 Surface integral computation
3.4.2 Analysis of extension and bending
3.4.3 Analysis of torsion
3.4.4 Deflection analysis
3.4.5 Modal analysis
3.4.6 Buckling analysis
3.5 Model 3: Cross-sectional finite element model
3.6 Model 4: 3D shell finite element model
3.6.1 Computation of cross-sectional stiffness matrix
3.6.2 Application to the experimental cross-sectional analysis
3.7 Summary of model capabilities
CHAPTER 4 DEVELOPMENT OF A NEW FINITE ELEMENT FOR THE EVALUATION OF CROSS-SECTIONAL PROPERTIES OF THIN-WALLED COMPOSITE BEAMS
4.1 Introduction
4.2 Review of the theory behind NABSA
4.2.1 Coordinate systems
4.2.2 Stress and strain
4.2.3 Internal loads
4.2.4 Generalized strain
4.2.5 Kinematics of the cross section
4.2.6 Strain-displacement relations
4.2.7 Principle of virtual work for a beam slice
4.2.8 Solution
4.2.9 Constraints to rigid body motion
4.2.10 Solving the problem for a given load case
4.2.11 Cross-sectional stiffness matrix
4.3 Implementation of the line finite element
4.3.1 Shape functions
4.3.2 Element coordinate system at node
4.3.3 Coordinate of a point in the element
4.3.4 Jacobian matrix
4.3.5 Displacement field, shape function and derivative of shape function matrices
4.3.6 Material properties
4.3.7 Numerical integration
4.3.8 Fictive rigidity for drilling degrees of freedom
4.3.9 Post-processing
4.3.10 Implemented elements
4.4 Validation of the implemented element
4.4.1 Validation case 1
4.4.2 Validation case 2
4.4.3 Validation case 3
4.4.4 Validation case 4
4.4.5 Validation case 5
4.4.6 Validation case 6
4.4.7 Validation case 7
4.4.8 Validation case 8
4.4.9 Validation case 9
4.4.10 Validation case 10
4.5 Conclusion
CHAPTER 5 COMPARISON OF DIFFERENT WIND TURBINE BLADE MODELS AGAINST EXPERIMENTAL RESULTS
5.1 Introduction and methodology
5.2 Model descriptions and cross-sectional properties
5.2.1 Model 1: simple model
5.2.2 Model 2: classical strength of materials model
5.2.3 Model 3: cross-sectional finite element model
5.2.4 Model 4: 3D shell finite element model
5.2.5 Experimental cross-sectional stiffness properties
5.2.6 Comparison
5.3 Natural frequencies
5.4 Deflection
5.5 Strains
5.6 Buckling
5.7 Composite Strength
5.8 Conclusion
CONCLUSION 

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