This paper describes the development of a continuous production energy
machine from marine trochoidal waves. Studying the characteristics of trochoidal
waves in a geographical area near Cartagena, we have developed a device, which
taking advantage of the marine surface oscillation in order to produce the movement
of a mechanical device, is able to transforming the mechanical energy into
electrical energy.Peer Reviewe

Gómez Lopera, S.A.

Inglés Inglés, C.

UPCommons. Portal del coneixement obert de la UPC

Design of a Continuous Production Energy Machine From Marine Trochoidal Waves C.  Inglés-Inglés*, S. A. Gómez-Lopera** Dep. of Applied Physics, Universidad Politécnica de Cartagena (UPCT), Campus Alfonso XIII, 30203 Cartagena, Spain *E-mail address: cii0@alu.upct.es**Corresponding author. Tel.: +34 968325599. E-mail address: salvador.glopera@upct.es Abstract - This paper describes the development of a continuous production energy machine from marine trochoidal waves. Studying the characteristics of trochoidal waves in a geographical area near Cartagena, we have developed a device which taking advantage of the marine surface oscillation in order to produce the movement of a mechanical system, is able to transforming the mechanical energy into electrical energy. Keywords – wave energy, point absorber, renewable energy, trochoidal waves I. INTRODUCTION  At present, the marine renewable energetic resources are one of the sets of power sources with an enormous potential. However, its exploitation is minimally developed. Its origin is constituted by the character of immense energy collector that form the seas and oceans, which occupy about 70% of the surface of the planet and storing on 1.3×109 km3 of water, are the largest existing energy reserves on earth and besides renewable [1]. The wave resource is ten times more energetic than solar or wind. In addition, its high energy density, high availability and low environmental impact are a good starting point to study a type of energy in continuous development [2]. In Spain they are also pursuing a number of projects in wave energy, a total of 26 were recorded in 2013, mainly on the coast of País Vasco, Cantabria, Galicia and the Canary Islands. Despite the lack of financial support to all renewable in Spain, big Spanish companies such as IBERDROLA, SENER or ABENGOA and research centers such as TECNALIA continue active in the ocean energy sector. There are also some enthusiastic small companies developing and testing wave and tidal current concepts. At a regional level, there is some support mainly from the two regional governments of the País Vasco  and Canary Islands. Their respective open sea test facilities, bimep and PLOCAN, are now fully prepared to install and test wave energy devices. Mutriku OWC plant in the País Vasco has now more than three years of continuous operation. There is further some initial interest in this field growing in other regions such as Andalucía and Galicia [3]. The operating principle of the device is being moved with a sinusoidal wave. The float and reciprocates by a mechanical system, connecting rod-crank, moving a generator rotor. This assembly is in a tight frame, supported on a structure at a given level of seabed [Fig. 1].  Fig.1. Point absorber in working  II. PROJECT DEVELOPMENT  Currently, existing technologies are very diverse, depending on the characteristics of the wave resource (wave height and period) and depending on the location of the device and the power selected for each unit. Therefore, the comparative advantage over existing systems is the use of a simple, robust, reliable and easy to maintain mechanism, leading to a reduction in costs. Moreover, its mechanical characteristics, the device performs as a continuous artifact energy production due to the pendulum movement that provides the wave for small wave heights. The type of device for the conversion of wave energy of this project is known as point absorber, i.e., two bodies that move vertically relative to each other by the effect of buoyant forces on bodies due to the wave elevations. The first body is called floater and is moved by the waves, while the second body, provides hydrodynamic stability,  1SIXTH INTERNATIONAL WORKSHOP ON MARINE TECHNOLOGY, Martech 2015Cartagena, September 15th, 16th and 17th - ISBN: 978-84-608-1708-6Page 153maintains its position against displacement of the waves. For the design of the energy absorber it is needed a hydrodynamic study at the location where it is desired to install, in order to find the most frequent wave height, besides analyzing the characteristics of the trochoidal wave [4]. This project, which is being developed as Final Degree Work, has focused on the coastal area of Cartagena (see Fig.1). In the same issue of the energy needs of small facilities, but also can be used to power autonomous systems and to reinforce conventional generation facilities studied.   Fig.2. Coastal area of Cartagena.. Analysis of wave characteristics, predictive, real-time and historical data [5]  The study of waves in the geographic area of Cartagena, in particular, Node WANA2074090 (Length: 0.833 E, Latitude: 37.500 N) [see Fig.3] near the beach Gorguel. The study of the implantation of the device in this area is because there is a fish farm and a core of houses without access to the electricity grid.   Fig.3. Coastal area of Cartagena, showing the selected node WANA2074090 [5] Focusing on the WANA2074090 Node, in order to study wave of the year 2014-2015, distributions of peak period (Tp) and height (Hs) has been presented in [Figs. 4 and 5].  Fig.4. Distributions of Height and wave Period   Fig.5. Statistics scalar wave series to the period 2014-2015 It is clear that the most often wave height generated is Hs = 1 m, with a wave period, Tp = 5 s. III. CHARACTERISTICS OF TROCHOIDAL WAVE Trochoidal waves are two-dimensional waves. In order to easily analyze changes in the characteristics of a wave as it propagates from the deep sea to the shore, it is necessary to consider [4]: • The water is homogeneous and incompressible, and surface tension forces are negligible. • Flow is irrotacional. Thus there is no shear stress at the air–sea interface or at the bottom. The velocity potential must satisfy the Laplace equation for two-dimensional flow: ² ² 0² ²x zφ φ∂ ∂+ =∂ ∂   (2)  where x and z are the horizontal and vertical coordinates, respectively. • The bottom is stationary, impermeable, and horizontal. • The pressure along the air–sea interface is constant.   2SIXTH INTERNATIONAL WORKSHOP ON MARINE TECHNOLOGY, Martech 2015Cartagena, September 15th, 16th and 17th - ISBN: 978-84-608-1708-6Page 154 Fig.6. Definition of progressive surface wave parameters Figure 6 depicts a monochromatic wave traveling at a phase celerity C on water of depth d in an x, z coordinate system. The X axis is the still water position and the bottom is at z = d. The wave surface profile is defined by z = η, where η is a function of x and time t. The wave length L and height H are as shown in the figure. Since the wave travels a distance L in one period T,  LCT=             (1) The horizontal and vertical components of velocity of the water particles at any instant are u and w respectively. The horizontal and vertical coordinates of a particle of water at any point are given by ξ and ε, respectively. The coordinates refer to the center of the orbital path that the particle follows. At any instant, the particle of water is at a distance d - (- z) = d + z above the bottom. In transitional to shallow water, the orbits reach the bottom and become elliptical with the ellipses becoming flatter near the bottom. At the bottom the particles follow a reversing horizontal path.   The following dimensionless parameters are often used: Wave number: 2kLπ=                 (3) Wave angular frequency: 2Lπσ =          (4) Using the Laplace equation, the velocity potential can be written as  cosh( ) sin( )2 coshgH d z kx tkdφ σσ+= −  (5)  Wave celerity and length for any given water depth and wave are 0 2gTC π=    (6) and 0²2gTL π=    (7)  The water particle velocity and acceleration as well as the pressure field in a wave are all needed to determine wave-induced forces on various types of coastal structures.  The horizontal and vertical components of water particle velocity (u and w, respectively) can be determined from the velocity potential where  ( ) cos( )sinhH coshk d zu kT kdπ x tσ+⎡ ⎤= −⎢ ⎥⎣ ⎦                    (8) ( ) sin( )sinhH sinhk d zw kT kdπ x tσ+⎡ ⎤= −⎢ ⎥⎣ ⎦                    (9)  In deep water the orbits are circular throughout the water column but decrease in diameter with increasing distance below the water surface, to approximately die at a distance sufficiently far.  Pressure field is ( ) cos( )2 coshgH coshk d zp gz kx tkdρρ σ+⎡ ⎤= − + −⎢ ⎥⎣ ⎦   (10)      The kinetic energy and potential energy for a unit width of wave crest and for one wave length are  ²16k pgH LE E ρ= =                        (11)  Energy in a wave per unit crest width E is  ²8c pgH LE E E ρ= + =            (12) Wave Power, P, the wave energy per unit time transmitted in the direction of wave propagation  is   212 sinh 2E KdPT k⎛ ⎞= +⎜⎝ ⎠d ⎟                      (13)  We have designed a prototype which has made some assumptions. Mainly it is concluded that the device is designed for a significant wave height that occurs most often in the place where you want to install.   3SIXTH INTERNATIONAL WORKSHOP ON MARINE TECHNOLOGY, Martech 2015Cartagena, September 15th, 16th and 17th - ISBN: 978-84-608-1708-6Page 155The characteristics of the trochoidal wave near to Cartagena area (Node WANA2074090, see [Fig. 3]) are shown in Table 1. The formulations described above were used for analysis which input values of measured buoy [5], as the period (Tp), the height of significant wave (Hs) and anchoring depth. Velocity potential, speed of particle and pressure field are presented in [Fig. 6], [Fig. 7] and [Fig. 8] respectively.  Table 1. Trochoidal wave characteristics near to Cartagena   Fig.6. Velocity Potencial. Eq. 5  Fig.7. The horizontal and vertical components of water particle velocity (u and w,) Eq. 8 and 9   Fig.8. Pressure Field in function of the position of wave length. Eq. 10  IV. PROTOTYPE DEVELOPMENT The design of the first prototype was made from reusable materials not therefore need not be non-functional as it produces a maximum of 5 volts (see [Figure 13]).   Fig.13. Design of prototype The project is currently in the phase of improving the design of the absorber and an experimental prototype. Manufacturing the prototype has been able to make the following conclusions (see Table 2) about our Point Absorber.   4SIXTH INTERNATIONAL WORKSHOP ON MARINE TECHNOLOGY, Martech 2015Cartagena, September 15th, 16th and 17th - ISBN: 978-84-608-1708-6Page 156Table 2. Representation of the advantages and disadvantages V. CONCLUSIONS In this paper we have designed and developed a continuous production energy machine from trochoidal waves. The study of waves is focused in the geographic area of Cartagena, in particular, at Node WANA2074090, near the beach Gorguel, to produce electricity at a fish farm and a core of houses without access to the electricity grid. The device is designed for a significant wave height that occurs most often in the place of interest. A competitive advantage with the current arrangements is a low price, because it uses a simple, sturdy rotary generating mechanism. This work is focused on the development of wave energy mechanisms with low environmental impact. VI. ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support from ETSINO, UPCT and the Organizing Committee of the MARTECH Workshop 2015. VII. REFERENCES [1] OEPM. Oficinal Española de Patentes y Marcas. Boletines OEPM / Energía marinas / Primer trimestre 2015. http://www.oepm.es/export/sites/oepm/comun/documentos_relacionados/Boletines/energias_marinas/2015_1_Trimestre_Energias_Marinas.pdf  [2] M. Lafoz, M. Blanco, P. Moreno –Torres, G. Navarro, C. Vázquez y L. García – Tabarés. Development of a project for direct convertion of wave energy into electricicity. Ingeniería Civil. 2014;176: 5-12. [3] OES. Ocean Energy Systems. Informe anual 2014. http://report2014.ocean-energy-systems.org/country-reports/spain/research-and-development/ [4] Sorensen, R.M (2006). Basic Coastal Engineering. Chapter 2: Two-Dimensional Wave Equations and Wave Characteristics. Springer US. Online ISBN: 978-0-387-23333-8. [5] Puertos del Estado. Government of Spain. http://www.puertos.es/eses/oceanografia/Paginas/portus.aspx [6]  Colli, V.D. , Cancelliere, P., Marignetti, F., Di Stefano, R., Scarano, M. (2006) “A Tubular-Generator Drive For Wave Energy Conversion” Industrial Electronics, IEEE Transactions on, Iune 2006. Vol 53 (4), pags. 1152-1159.  [7] J. Falnes, Ocean Wave Energy and Oscillating Systems: Linear Interaction Including Wave-Energy Extraction, 1st ed. Cambridge, U.K.: Cambridge Univ. Press, 2002.  5SIXTH INTERNATIONAL WORKSHOP ON MARINE TECHNOLOGY, Martech 2015Cartagena, September 15th, 16th and 17th - ISBN: 978-84-608-1708-6Page 157

Design of a continuous production energy machine from marine trochoidal waves

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