Finite Element Analysis of a Kite for Power Generation

Finite Element Analysis of a Kite for Power Generation

Bosch, H.A.

Tiso, P. (mentor)
Schmehl, R. (mentor)
Rixen, D.J. (mentor)
Zadpoor, A.A. (mentor)

Mechanical, Maritime and Materials Engineering

Precision and Microsystems Engineering

2012-04-05

The kite is modelled with the non-linear finite element method to stay close to its physical properties and represent its full non-linear flexible behaviour. The inflatable beams in the leading edge and struts are modelled with regular beam elements that represent the behaviour to reduce the amount of degrees of freedom drastically. The canopy is modelled with shell elements and uses a coarse mesh to reduce the computation time without losing essential deformation modes. The aerodynamic model of Breukels [7] is used to describe the distributed aerodynamic forces exerted on the kite depending on its deformation. The model is based on the assumption that the kite can be divided into a finite number of two dimensional wing sections. The aerodynamic properties are determined for each wing section from a set of two dimension CFD experiments and distributed over the wing section using a set of weight factors. The finite element kite model and aerodynamic model form a fluid-structure-interaction problem together that needs to be solved iteratively. A solving algorithm is introduced that splits the structural and aerodynamic convergence and uses a load stepping algorithm to stabilize and speed-up convergence. The bridles and tether are modelled dynamically as simple spring-dampers using multi-body dynamic methods. The end of the bridles are connected to the kite at the bridle attachment points. The most important reduction principle is the assumption that the kite reacts quasi-static to the aerodynamic forces, because the inertia of the kite are very small compared to the aerodynamic forces. Therefore the local inertia of the kite are neglected when solving the finite element equations and the dynamic deformations of the kite can be approximated by a sequence of static solutions. The quasi-static fluid-structure-interaction problem returns forces that are exerted on the end points of the bridles in the dynamic simulation. These forces are assumed to remain constant during the period of a time step, eliminating the need to solve the fluid-structure-action problem in the dynamic differential equations. This method greatly reduces the amount of computation time, because the time integration only has to be done for the small number of degrees of freedom in the dynamic model and the fluid-structure-interaction problem only needs to be solved once in every time-step instead of multiple times in the time integration algorithm. All system components were implemented in Matlab and a controller was built to fly several figure eight tests with the model. Results show that the modelling approach leads to a fast and realistic model. A steering input results in dynamics and a real deformation that causes the kite to yaw comparable to real kites and other models. It can be concluded that all the assumptions were valid and led to a model that captures the kite behaviour realistically. The model is a factor 25-30 slower than real time, which is very fast considering the complexity of the calculations and that it was implemented in a non compiled language. The clearly visible distinct deformation modes and non-linear force model make it also a suitable and interesting candidate for further new model reduction techniques. The aerodynamic model has some shortcomings resulting in an overestimation of the lift over drag ratio and is considered to be the main source of uncertainties in the whole model. Replacement with a better model should further improve the model and make it possible to do an extensive validation study. Concluding, the new proposed approach is successful: fast and realistic, flexible in its use, able to model all type of kites, a good candidate for further reduction and can be used for controller design and optimizing studies.

finite element analysis
power generation

http://resolver.tudelft.nl/uuid:888fe64a-b101-438c-aa6f-8a0b34603f8e

2012-05-31

Student theses

master thesis

(c) 2012 Bosch, H.A.