Modeling Wind Turbine Blades for Fluid/Structure Interaction Analysis

Eolos Researchers in the University of Minnesota’s Department of Civil Engineering are developing a novel computational model for describing the structural behavior of wind turbine blades by applying behaviors typical of shell structures to the more straightforward beam theory. Wind turbine blades are thin-walled structures and, as such, are properly classified as shell structures. However, the ratio of their span length (approximately 45 meters) to chord length (1 to 3 meters) is more typical of a structural beam than a shell. In practice, both shell and beam models are used to analyze wind turbine blades.

With the goal of capturing ever more power from the wind, wind turbine manufacturers are extending blades lengths to 45 meters and longer.  However, with increased blade length comes with an increase in mass, blade flexibility, structural forces, and a ¬¬potential for decrease in operating lifetime due to fatigue damage.  In order to account for all these factors, turbine manufacturers will need to better understand how blades react to static and dynamic forces.
 
When a blade is subjected aerodynamic forces, the blade will undergo a deformation as the structure is inherently flexible.  With the complexity of the geometry and material used in wind turbine blades today, it is difficult to predict how much the blade will deflect.  It is crucial in the design process, therefore, to develop tools capable of predicting how a turbine blade will react to these forces.

The objective of this project is to develop a computational model that can account for the structural dynamics of a typical wind turbine blade. In addition, the parameters of this model can be easily modified for experimentation with various design options of blades.

Beam versus Shell
Approaches for blade modeling utilize both beam models and shell models. The choice between these two models depends on the particular objective of the analysis. The shell model is necessary for investigating details of the blade’s local response, such as buckling or delamination (the separation of layers of the composite materials). However, in a typical operating environment, the overall response of a structurally-sound blade is much like that of a beam. Using a beam model is significantly simpler than the simplest of shell models and is adequate for many investigations. For example, a beam model may be used to explore the blade-fluid interaction, where the objective is to identify forces acting on the blade or details of fluid (air or water) flow around the blade. The results of such analysis can then be used to optimize the parameters of the blade design in order to improve performance and increase power output.

Beam theories can be devised or modified to account for various features of beam composition. The geometric and material compositions of turbine blades have many features that are different from those of beams found in structures such as bridges or buildings. In addition to being thin-walled, the blades have variable and multi-cellular cross-sections that can change abruptly, the wall of the blades typically has variable thickness, and the material of the wall may be different in different parts of the blade (even within a single cross-section).
 

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Figure 1: The new model will allow researchers to predict blade deformation such as that shown in this picture.
 

The model developed through this research is a combination of the standard beam and the finite element shell models. The beam component is described by a simple theory (called Euler-Bernoulli beam theory). The model is enriched by including the deformation pattern called warping, described using the finite element methodology. The finite element technique is based on the idea that an accurate representation of a quantity, such as displacement, temperature, or force, over the entire surface area of the blade can be achieved by the knowledge of that quantity at a large number of points on that surface. The finite element technique depends on having knowledge of a sufficient number of points. While thin-walled beam models that account for warping exist, they are typically subjected to various simplifying assumptions and restrictions which are incompatible with the design process of turbine blades. In addition, they are often too cumbersome to be effective for the purpose of exploring various design options. In the model developed in this project, such restrictions are not present and experimentation with various designs is made easy by describing warping using the finite element points. An additional advantage of this approach is that the points used in the finite element analysis are compatible with the data required by blade fabricators in the process of construction.
 

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Figure 2: The blades of the Eolos wind turbine wait to be installed at the UMore Park field site.  This photo shows the complicated cross-sections of the blades.


Researchers at the St. Anthony Falls Laboratory have since converted the code that was initially developed in Matlab into C++ so that it can be applied to models of fluid motion around the turbine. The ultimate goal is to create a program that considers the fluid-structural interaction between the air and the blade, so that users can input information about the wind and have the program predict the blade response. At present, the model assumes a stationary blade with wind flowing around it.

Next steps for this research include accounting for complexities such as the effect of the turbine tower and the motion of the blade in the model, as well as customizing the program to a particular blade shape.
 

Ariel Dahl
Professor Henryk Stolarski