WIND TURBINE BLADE DESIGN USING FEM

Transcription

1 WIND TURBINE BLADE DESIGN USING FEM By: Wei Cheng Wenyu Zhou Afolabi Akingbe May 1,

2 1. Abstract The energy output of wind turbines is directly affected by the structural design of the turbine. Due to heavy mechanical loads and the nature of the wind, the mapping of stress and strain of wind turbines and the dynamic effect of the structure become critical. When designing a wind turbine, using appropriate finite element modeling can help produce the desired simulation of the structure so as to ensure a certain level of structural safety. Shell element is a particular model that is presented in this problem. Also the modification of the blade shape in ANSYS is one of the common approaches that we will exhibit in this paper to analyze the turbine structure. 2. Introduction As a popular and rapidly growing sector in renewable energy field, wind power is emission-free and inexhaustible. To produce energy, a wind turbine is utilized to convert power that is extracted from the wind to mechanical power and then electrical power. Due to the various loads and large stresses that a wind turbine is subject to, its structural behavior and dynamics in operation needs to be considered. The ultimate goal for turbine engineers is to enhance the turbines performance by maximizing the life and power coefficient and minimizing the drag coefficient while ensuring the structural stability and robustness of the turbines. The aerodynamic performance of a wind turbine is significantly dependent on the design of the blades, and the structural strength and stiffness and fatigue of the blade are also crucial to operation and lifetime of the wind turbines. In the design part, Blade Element Momentum Theory (BEM) is performed to achieve the basic geometry of a wind turbine blade. To examine a blade s deformation and stress distribution, we implemented Finite Element Method (FEM) for analytical solution. Apart from analysis using FEM and BEM theories, commercial software ANSYS Structural has been implemented as well to present a three dimensional blade model for visual aid on the displacement and stress distributions. 3. Background of wind turbines When air flow comes to the wind turbine blades, it creates lift forces that push the blade to rotate, therefore generating electrical power. Meanwhile, it also creates drags those are expected to be minimized. Since the turbine s performance is significantly dependent on the shape of a blade, the blade geometry is critical improving wind turbines efficiency. The blade shape is designed to be to satisfy the need of creating more lift without inducing too much drag. In the basic wind turbine shape design, two geometric 2

3 parameters are included, namely chord and twist angle. Viewing from the tip of a blade, one can observe that the blade s chord gets larger while maintaining twist angles. Here, we have used Blade Element Momentum Theory to generate the basic blade shape. A blade was discretized into finite elements. For each element, BEM was implemented to compute the lift and drag forces, chord and twist angle. Then the elements are integrated along the blade to present a blade geometry based on the chords values. After the basic blade shape was determined, we performed analytical solution implementing finite element method to examine the structural behavior of a blade. 4. Shell element a) Shell element in FEM As is known that a wind turbine blade performs better with lighter structural composition, it is reasonable that the structure is built hollow. With such structural requirement, shell elements are especially useful tools in modeling the behavior of the interest. A shell element exhibits the behavior combining a membrane element for plane elasticity and a bending element for plate theory, where both plane and bending deformation are believed extensively applied on a typical wind turbine blade. In the classic flat shell element formulation, a quadrilateral shell element is proposed. The derivation of the theory will be attached in appendix. b) Shell element in blade Given the primary part of the blade is made in shell, the function of the shells is not only to provide the aerodynamic shape, but also play a structural role in stiffening and strengthening the whole blade, particularly to resist a great amount of torsion. Also, blade shells together with spar boxes are significantly useful in the respect of resisting bending. Blade shell also decides the weight of the structure to a certain extent, whilst the shells can support the edgewise bending stresses for most of the length of the blade and it s self-weight. And therefore, to account for all the potential failure stated above, the blade analysis with a full scale stress profile or displacement is crucial to the design process. 5. ANSYS results To analyze the properties and reactions of the wind blade, we use the commercial software ANSYS. This finite element tool is used because we find it to be excellent for obtaining an analysis for different geometries and properties of an object. We feel that once we have the geometries ready, we can swap them in and out easily to observe how 3

4 they affect the performance of the wind blade. We can also change the material of the blade using this tool, which allows us to analyze how different materials affect the results. In our model of the wind blade, we believed that it is best to have it thicker at the base of the blade and thinner at the tip. If the blade would move like a cantilever beam, there would be more stress at the base than at the tip. Having it thicker at the base would help it withstand higher loads better. Fig Thickness of the blade To model the wind blade subject to the environment it is placed in, we applied pressure and moments on it. Fig The pressure and rotational velocity applied to the wind blade design. Pressure with varying magnitudes was applied onto the blade to simulate the wind that flows into the structure. Since the blade is fixed to the hub of a wind turbine, we fixed the hub end of the blade to prevent movement and added a rotational velocity at that point to simulate the moment acting at that point. After using ANSYS to solve the geometry, we got an idea of how the wind turbine reacts when subject to different loads. As we thought, higher stress is located closer to the hub than the tip. However, the highest stresses are not only found at the blade root but also at the area where the geometry get wider. This shows that extra care must be considered at areas where there is a sharp change in the width of the blade. We also discovered that one side of the blade is subject to more stress than the other side, creating lift that allows the wind turbine to rotate. 4

5 Fig Total Stress on the blade. 6. Conclusion and Future Work One powerful feature of ANSYS is that one can experiment different materials on different elements based on specific need. For example, the root of a blade is subject to a concentration of stress, so a more robust and rigid material should be considered when one designs the root. Also, for further study we could experiment with different designs of wind blades to optimize the shape for use in different locations. 7. References Cai, X., Zhu, J., Pan, P., & Gu, R., 2012, Structural optimization Design of Horizontal-Axis Wind Turbine Blades Using a particle Swarm Optimization Algorithm and Finite Element Method, Energies, v. 5, p El Chazly, N. M., 1993, Static and Dynamic Analysis of Wind Turbine Blades Using the Finite Element Method, Computers & Structures, v. 48, p Nguyen, N., Rabczuk, T., Nguyen-Xuan, H., & Bordas, S. P. A., 2008, A smoothed finite element method for shell analysis, computer methods in Applied Mechanics and Engineering, v. 198, p

6 7. Appendix Appendix 1 Derivation of the finite element analysis for shell element In the bounded domain Ω, a flat shell element shall be considered in the following local coordinate system x-y-z, with six degrees of freedom sourcing simultaneously from membrane and bending actions. Fig.7.1. An illustration of shell element subject to plane membrane and bending action: (a) plane deformation, (b) bending deformation Fig.7.2. An illustration of degrees of freedom of a plate and plate (bending) and plane stress (membrane) finite element in local element-aligned coordinate system With the proper derivation, starting with the formation of membrane ϵ m, curvature κ and transverse shear strain γ matrices, 6

7 together with the finite element solution model for the flat shell, which is expressed as of a displacement where np is the total number of element nodes, Ni are the bilinear shape functions associated to node i and are the nodal degree of freedom of u h associated to node i, the approximation of the strain field, the discrete curvature field and the shear strain can be computed and listed accordingly as following strain field: discrete curvature field: shear strain: 7

8 Combining simultaneously membrane and bending action, a linear system for the vector of nodal unknowns q, where k e is the stiffness matrix composed of membrane and plate stiffness element matrices: and the load vector at each node i is of the form: with And these key matrices set the foundation for further steps of assembly and machine computation. 8