# Design and Analysis of Wave Energy Converter

### Motivation

In the age of energy transition, renewable energies are playing an increasingly important role. As a result of this, hydropower, solar and wind energy are becoming more important. In addition to these well-known examples of renewable energies, there is also the possibility to generate energy from ocean waves. Thereby, mechanical systems are positioned on the sea surface, which are subjected to an up and down movement by the arising waves. An internally installed electrical generator converts then this movement into electrical voltage. Since wave energy has a notably high power density compared to wind and solar energy, it has been recognized as one very promising resource of renewable energies.

In order to be able to generate as much energy as possible, mechanical systems have to be constructed in such a way that they experience a large movement by the incoming waves. For this purpose, it must be clarified which waves arise in the open sea and which forces they affect on a given mechanical system. At the Institute of Mechanics and Ocean Engineering, two systems are available for which this has to be investigated.

### Modeling of water waves

There are many different methods available for modeling water waves. Probably the simplest approach is a linear summation of sine waves, which are all randomly phase-shifted to each other. If the corresponding amplitudes are chosen appropriately, the real sea can be simulates relatively well.

However, a closer look at the sea surface shows that especially higher waves appear much more frequently than predicted by linear wave theory. As a consequence of this, nonlinear wave theories are used to describe the behavior of water waves as good as possible. Thereby, different aspects like the influence of wind or the interaction of water waves can be considered.

*A nonlinear wave that appear out of nowhere and triples its amplitude in a very short time (left) and two waves that interact and then return to their orginal shapes (right).*

With respect to the generation of energy from ocean waves, it is necessary to find out which waves exert which forces on a given mechanical system. In order to calculate the fluid-structure interaction occurring in the environment of a natural sea state, different methods of Computational Fluid Dynamics (CFD) are used.

### Wave energy converter

To build a mechanical system that extracts energy from water waves, an electrical generator uses either the translational or rotational motion of the system. At the Institute of Mechanics and Ocean Engineering experimental setups for each of these possibilities have been developed and are the basis of further investigations.

The first setup consists of a fixed coil and a movable magnet attached to a floating cylinder. If the cylinder is moving up and down by an incoming wave, the magnet moves in the same proportion through the coil and voltage is induced. The aim is to find out which waves of which frequency and amplitude have which effects and how to change the system to generate as much energy as possible. Parameters such as the mass and the lift volume of the cylinder as well as the electronic damping of the generator can be changed to maximize the generated energy.

This setup is located in the institute's own wave channel and can be tested for a wide range of given waves.

*View on the floating cylinder in the wave flume.*

A simulated random sea surface and the corresponding heave motion of the cylinder.

The second setup presents a pendulum energy converter, which embodies a tri-pendulum design with three arms at equal 120° spacings. The test bench is capable of exciting the pivot of the pendulum by large amplitude random motion which can for example accurately simulate ocean waves. Moreover, several different parameters can be adjusted, like the inclination of the plane of rotation and positions of additional masses, which change the moment of Inertia of the pendulum system. An attached generator then produces electrical energy. Again it has to be tested, how different mechanical and electrical parameters have to be chosen in order to generate as much energy as possible.

Test bench of the pendulum energy converter.

* **Measured angle of the pendulum, whereby the pivot of the pendulum is excited by a realistic ocean wave. The green regions indicate rotation of the pendulum. For further details, see: L. Dostal, M.-A. Pick. Theoretical and Experimental Study of a Pendulum Excited by Random Loads. In: European Journal of Applied Mathematics 30 (2019), No. 3, 912-927.*

*Probability to reach rotational motion in dependence of wave height, wave frequency and initial position. For further details, see: L. Dostal, K. Korner, E. Kreuzer, D. Yurchenko. **Pendulum Energy Converter Excited by Random Loads. In: ZAMM-Journal of Applied Mathematics and Mechanics 98 (2018), No. 3, 349-366. *

### Student Involvement

This topic represents an interface between the fields of mechanics, electrical engineering, control engineering, numerics and fluid dynamics and offers much space for student works. Depending on your interests, you can either work on the modeling of water waves, fluid-structure interaction, control/optimization of system parameters or the design of a more efficient electrical generator. Who knows, you might even have your own ideas on how to draw energy from water waves. If you are interested to contribute to this topic within the scope of a project work or a Bachelor-/Masterthesis, please contact us.

### Student Projects, Theses and Visiting Scholars

*Zetek, C.:*"Numerical analysis of the fluid-structure interaction for different shapes of the floating body", Bachelor Thesis, BSC-XXX, 2021.*Höhne, J.:*"Simulative study and of the motion of a multi-component wave energy converter in random waves", Bachelor Thesis, BSC-XXX, 2021.*Engel, J.:*"Simulative study and control of the motion of a multi-component wave energy converter in three dimensions", Bachelor Thesis, BSC-XXX, 2021.*Sprengell, Anneke:*"Numerical Study of a Multi-Harvester-System for Wave Energy Conversion", Bachelor Thesis, BSC-129, 2021.*Gohle, Simon:*"Effects of the shape of a cylindrical floating body

on the acting hydrodynamic forces", Bachelor Thesis, BSC-128, 2021.*Shamko, Pavel:*„Simluative investigation of the dynamics of a wave energy converter in regular waves“, Bachelor Thesis, BSC-125, 2020.*Bluhm, Benedict:*„Analysis and optimization of the dynamics of a kinetic wave energy conveter“, Bachelor Thesis, BSC-124, 2020.*Woidelko, Mirco:*„Wave energy converter enlargement using reinforcement learning“, Bachelor Thesis, MSC-XXX, 2020.*Yang, Zhengyi:*„Systematic study of the performance of a wave energy converter“, Bachelor Thesis, BSC-118, 2020.*Kühne, Christian:*„Simulative and experimental investigation of the dynamics of a wave energy converter using flexible multibody systems“, Bachelor Thesis, BSC-118, 2020.*Schulz, Leonard:*„Development, modelling and simulation of a novel, cost-effective and reliable wave energy converter“, Bachelor Thesis, BSC-116, 2020.*Heidler-Behne, Nico:*„Systematic study of a wave energy converter“, Bachelor Thesis, BSC-110, 2020.*Thomsen, Nele:*„Computation and comparison of linear and nonlinear water waves“, Bachelor Thesis, BSC-108, 2019.-
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*Fischer, Hendrik:*„Analysis of the Interaction of weakly nonlinear water waves“, Bachelor Thesis, BSC-107, 2019. -
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*Laketa, Samuel (Waterloo):*„ Development of a suitable generator for a Pendulum Energy Converter“, Visiting Scholar, 2019. -
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*Champenois, Bianca (Berkley): „*Pendulum Energy Converter Excited by Water Waves“, Visiting Scholar, 2018. -
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*Bespalko, Alexej:*„Systematic investigation for a Reinforcement-Learning based Regulation of an Acrobot“, Bachelor Thesis, BSC-093, 2019. -
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*Hollm, Marten:*„Investigation of weakly nonlinear water waves under stochastic wind excitation”, Master Thesis, MSC-018, 2018. -
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*Cyr, Carolin (Hoboken):*„Influence of nonlinear water waves on an energy converter“, Visiting Scholar, 2018. -
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*Korner, Kevin (Pasadena):*„Pendulum energy converter excited by random loads“, Visiting Scholar, 2018.

### Selected Publications

- L. Dostal, M. Hollm, E. Kreuzer: Study on the behavior of weakly nonlinear water waves in the presence of random wind forcing. In:
*Nonlinear Dynamics*(2019). [DOI:10.1007/s11071-019-05416-5] -
· L. Dostal, M.-A. Pick: Theoretical and Experimental Study of a Pendulum Excited by Random Loads. In:

*European Journal of Applied Mathematics*30 (2019), No. 3, 912-927. -
L. Dostal, K. Korner, E. Kreuzer, D. Yurchenko: Pendulum Energy Converter Excited by Random Loads. In:

*ZAMM-Journal of Applied Mathematics and Mechanics*98 (2018), No. 3,349-366. [DOI:10.1002/zamm.201700007] - L. Dostal, M.-A. Pick: Power Generation of a Pendulum Energy Converter excited by Random Loads. In:
*Proceedings of the 9th European Nonlinear Oscillations Conference*(Budapest, Hungary, June 25-30, 2017). -
· L. Dostal: Probabilistische Analyse der nichtlinearen Dynamik von Schiffen im natürlichen Seegang. Doktorarbeit, TUHH, Shaker Verlag, 2016.