Marine Systems & Ocean Technology Journal of SOBENA

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2 Marine Systems & Ocean Technology Journal of SOBENA Adress: Av. Presidente Vargas, Grupo 709 a Centro - Rio de Janeiro - RJ - Brasil - CEP Telephones: [+55](21) Telefax: [+55] (21) sobena@sobena.org.br - Site: List of Editors Celso Pupo Pesce Universidade de São Paulo, Brazil (Chief-Editor) ceppesce@usp.br Marcelo de Almeida Santos Neves Universidade Federal do Rio de Janeiro, Brazil (Chief-Editor) masn@peno.coppe.ufrj.br Michael M. Bernitsas University of Michigan, USA michaelb@engin.umich.edu Belmiro Mendes de Castro Filho Universidade de São Paulo, Brazil bmcastro@usp.br Günther Clauss Technical University of Berlin, Germany clauss@naoe.tu-berlin.de Paulo de Tarso Temístocles Esperança Universidade Federal do Rio de Janeiro, Brazil ptarso@peno.coppe.ufrj.br Segen Farid Estefen Universidade Federal do Rio de Janeiro, Brazil segen@lts.coppe.ufrj.br Odd Faltinsen Norwegian University of Science and Technology, Norway oddfal@marin.ntnu.no Jeffrey M. Falzarano Texas A&M University, USA jfalzarano@civil.tamu.edu Antonio Carlos Fernandes Universidade Federal do Rio de Janeiro, Brazil acfernandes@peno.coppe.ufrj.br José Alfredo Ferrari Jr Petrobras, Brazil jferrari@petrobras.com.br André Luiz C. Fujarra Universidade de São Paulo, Brazil afujarra@usp.br Carlos Guedes Soares Universidade Técnica de Lisboa, Portugal guedess@mar.ist.utl.pt Atilla Incecik Universities of Glasgow & Strathclyde, UK atilla.incecik@na-me.ac.uk Breno Pinheiro Jacob Universidade Federal do Rio de Janeiro, Brazil breno@coc.ufrj.br Jan Otto de Kat A. P. Moeller-Maersk, Denmark jean.dekat@maersk.com Carlos Antonio Levi da Conceição Universidade Federal do Rio de Janeiro, Brazil levi@peno.coppe.ufrj.br Clóvis de Arruda Martins Universidade de São Paulo, Brazil cmartins@usp.br Júlio Romano Meneghini Universidade de São Paulo, Brazil jmeneg@usp.br Torgeir Moan Norwegian University of Science and Technology, Norway tormo@marin.ntnu.no Helio Mitio Morishita Universidade de São Paulo, Brazil hmmorish@usp.br Celso Kazuyuki Morooka Universidade de Campinas, Brazil morooka@dep.fem.unicamp.br Kazuo Nishimoto Universidade de São Paulo, Brazil knishimo@usp.br Apostolos Papanikolaou National Technical University of Athens, Greece papa@deslab.ntua.gr Floriano Carlos Martins Pires Jr Universidade Federal do Rio de Janeiro, Brazil floriano@peno.coppe.ufrj.br Claudio Ruggieri Universidade de São Paulo, Brazil claudio.ruggieri@usp.br Claudio Mueller Prado Sampaio Universidade de São Paulo, Brazil clasamp@usp.br Alexandre Nicolaos Simos Universidade de São Paulo, Brazil alesimos@usp.br Sergio Hamilton Sphaier Universidade Federal do Rio de Janeiro, Brazil sphaier@peno.coppe.ufrj.br Célio Taniguchi Universidade de São Paulo, Brazil taniguch@usp.br Eduardo A. Tannuri Universidade de São Paulo, Brazil eduat@usp.br Pandeli Temarel University of Southampton p.temarel@soton.ac.uk Armin Walter Troesch University of Michigan, USA troesch@umich.edu José Márcio do Amaral Vasconcellos Universidade Federal do Rio de Janeiro, Brazil jmarcio@peno.coppe.ufrj.br Dracos Vassalos University of Strathclyde, United Kingdon d.vassalos@strath.ac.uk Murilo Augusto Vaz Universidade Federal do Rio de Janeiro, Brazil murilo@peno.coppe.ufrj.br Ronald W. Yeung University of California at Berkeley, USA RWYeung@Berkeley.edu

3 Volume 9 Number 2 December 2014 Chief-Editors Marcelo de Almeida Santos Neves Universidade Federal do Rio de Janeiro Celso Pupo Pesce Universidade de São Paulo JOURNAL OF SOBENA Sociedade Brasileira de Engenharia Naval

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5 Aims and Scope The design process of marine systems is one of formulation, evaluation and modification. Very often the problems confronting the designer are effectively complex problems, particularly on the technical side. Analytical models have to be invoked and applied together with numerical and experimental simulations, guided by intelligent experience, at all levels of the design chain. In the past these difficulties have been more concentrated on few particular types of marine vehicles and systems. In particular, naval architects have designed surface ships. Specialised methodologies and rules have been developed and accumulated in this field. Some excellent periodicals are dedicated to the coverage of researches and developments in this sector. More recent technological developments, particularly in the offshore industry, have challenged this knowledge, introducing many, and often radically distinct departures from the more conventional designs. Hence, largely multidisciplinary technologies are presently at the frontline, demanding fresh contributions not only from the naval architecture and ocean engineering fields, but also from all contributing areas as civil, mechanical, electrical, material, petroleum, coastal and oceanographic engineering, applied oceanography and meteorology and applied mathematics. Marine Systems & Ocean Technology intends to contribute to this wide and rich technological scenario by providing a forum for the discussion of mathematical, scientific and technological topics related to: hydrodynamic and structural analysis of any fixed and floating marine systems (including ships and advanced marine vehicles), underwater technology (including submarines, robotics, design and operation of diving systems, surveys and maintenance systems, umbilical cables, pipelines and risers), computational methods in naval architecture, offshore/ocean engineering, coastal engineering and related areas, environmental studies associated with oil spills and leakage prevention and control, safety concepts and risk analysis applied to marine systems, wave-energy extracting devices and sea resources in general, ocean and river transportation economics, marine engineering and environmental protection, offshore support bases, offshore logistics. Marine Systems & Ocean Technology is an editorial initiative jointly coordinated by SOBENA and CEENO. SOBENA is an abreviation for Sociedade Brasileira de Engenharia Naval, a learned society founded in 1962 for promoting technological development. CEENO is a Scientific Network on Naval Architecture and Ocean Engineering organized in 1999 by leading members of the Brazilian scientific community afiliated to two universities and two research centers: COPPE/UFRJ, USP, IPT, CENPES. Marine Systems & Ocean Technology (ISSN X) is published twice a year and is owned by Sociedade Brasileira de Engenharia Naval - SOBENA, and is distributed freely to members. Rate for 2011 is R$ for institutions and R$ for individuals. Issues are airmail shipped. All subscriptions are payable in advance and entered on an annual basis. Copyright 2005 by Sociedade Brasileira de Engenharia Naval. Printed in Brazil. Authorization to photocopy articles may be granted by Sociedade Brasileira de Engenharia Naval, provided the material is used on a personal basis only. The Society does not consent copying for general distribution, promotion, for creating a new work or for resale. Permission to photocopy articles must be requested to the SOBENA main office. Marine Systems & Ocean Technology

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7 Computational modeling applied to the study of wave energy converters (WEC) Flávio Medeiros Seibt 1, Max Letzow 1, Mateus das Neves Gomes 2,3, Jeferson Avila Souza 1,4, Luiz Alberto Oliveira Rocha 1,3,4, Elizaldo Domingues dos Santos 1,4 and Liércio André Isoldi 1,4,* 1 Programa de Pós-Graduação em Engenharia Oceânica (PPGEO) - Escola de Engenharia (EE), Universidade Federal do Rio Grande (FURG), Av. Itália km 8, CEP , Rio Grande-RS, Brazil. 2 Instituto Federal de Educação, Ciência e Tecnologia do Paraná (IFPR) 3 Programa de Pós-Graduação em Engenharia Mecânica (PROMEC) - Universidade Federal do Rio Grande do Sul (UFRGS) 4 Programa de Pós-Graduação em Engenharia Oceânica (PPGEO) - Escola de Engenharia (EE), Universidade Federal do Rio Grande (FURG), Av. Itália km 8, CEP , Rio Grande-RS, Brazil. * Corresponding Author: liercioisoldi@furg.br Abstract The employment of numerical methods to solve engineering problems is a reality, as well as, the worldwide concern about the need of renewable and alternative energy sources. Thus, this work presents a computational model capable of simulating the operating principle of some Wave Energy Converters (WEC). To do so, the device is coupled in a wave tank, where the sea waves are reproduced. The Finite Volume Method (FVM) and the Volume of Fluid (VOF) model are adopted. The results showed that the converter's operating principle can be numerically reproduced, demonstrating the potential of computational modeling to study this subject. Keywords Computational Modeling, Volume of Fluid (VOF), Wave Energy Converters (WEC), Oscillating Water Column (OWC), Overtopping, Submerged Plate. Nomenclature g Gravitational acceleration Velocity vector H Wave height x Horizontal direction H p Plate installation height w Velocity component of the wave in z direction h Water depth z Vertical direction k Wave number Volume fraction L Wave length Viscosity p static pressure π Mathematical constant T Wave period Density t Time Stress tensor u Velocity component of the wave in x direction Angular frequency Vol. 9 No. 2 pp December 2014 Marine Systems & Ocean Technology 77

8 Computational modeling applied to the study of wave energy converters (WEC) Flávio Medeiros Seibt, Max Letzow, Mateus das Neves Gomes, Jeferson Avila Souza, Luiz Alberto O. Rocha, Elizaldo Domingues dos Santos and Liércio André Isoldi 1 Introduction In the discussions about the energy issue, deepened by the oil shortages and climate changes, caused by the fossil fuel combustion, arises the need of researches and studies seeking the scientific and technological developments for the use of renewable and alternative energy sources (Pacheco, 2006). In this context and considering the potentiality of the region where Federal University of Rio Grande (FURG) is located (in the south of Brazil), researches concerning the conversion of the sea wave energy into electrical energy have been developed in this university since The exploration of the enormous energy reserve of sea waves represents an innovation domain, where almost everything still need to be developed. Theoretically, if it were possible to equip the planet coastlines with Wave Energy Converters (WEC), the existing power plants could be disabled. The value of existing energy resource in the seas becomes extremely attractive if one considers that the total amount of wave power is around 2 TW, a value that is equivalent to the annual average electrical power consumed worldwide. This value is distributed unevenly around the world, being its evaluation estimated in terms of power per length of wave front (kw/m). The average power of waves occurs mostly in moderate to high latitudes and has one potential between 40 and 100 kw/m (Cruz and Sarmento, 2004). Specifically in southern coast of Brazil there is an availability around 30 kw/m, being a possible source of renewable and alternative energy to the region. It is well known that to the analysis of engineering problems, such as the sea wave energy conversion into electrical one, three approaches are possible: the analytical methods, the numerical methods and the experimental methods. However, the analytical methods usually can be used only in problems in which the required simplifications hypothesis causes great deviations from the real physical phenomenon. Besides, its use is restricted to simple geometries and simple boundary conditions. On the other hand, experimental methods deal with the real configuration of the problem, but they are extremely expensive and often cannot be applied due to security issues or due the difficulty to reproduce the real conditions. Then, the use of numerical methods arises as a powerful tool to help in the solution of engineering problems. Virtually, they don't present restrictions and have the capability to quickly solve complex problems, with varied boundary conditions and defined in complex geometries (Maliska, 2004). It is obvious that the analytical solutions should not be discarded, being one of its important applications in the verification process of numerical models, helping the development of more robust numerical methods. Likewise and wherever possible, the experimental results should be used to validate the computational models. Therefore, what should be practiced in engineering is the combination of these three techniques, resulting in a better design with lower cost. There are no doubt that this is the way of modern engineering, in which the numerical simulation will perform, increasingly, a decisive role in the cost and quality of the project, walking side by side with the laboratory experiments (Maliska, 2004). Thus, the goal of this work is to present the computational model that have been used by the FURG research group for the analysis of the operating principle of WEC. To do so, three different types of these devices were numerically studied: the Oscillating Water Column (OWC), the Overtopping device and the Submerged Plate. In this sense, it was possible to show the computational modeling potential to accurately reproduce the operational principle of these converters, allowing the realization of several other studies and investigations about wave energy conversion. 2 Computational modeling The computational modeling simulates physical phenomena employing a systematic which involves engineering, mathematical and computer science. The physical phenomenon that will be studied is represented by a differential equations system (translation of the engineering problem to mathematics). This equations system is approximated by a discretization method (translation of the mathematical problem to computer science). Finally, the numerical simulation results are compared with the studied physical phenomenon (translation of the computer science problem to engineering) (Devloo, 2005). Therefore, to obtain an approximated numerical solution it is necessary to use a discretization method that approximates the differential equations by means of an algebraic equations system, which is computationally solvable. The approximations are applied to small domains in space and/or time, and then the numerical solution generates results in discrete locations in space and in time (Ferziger and Perić, 1997). The computational model presented in this work was developed in GAMBIT and FLUENT package. The GAMBIT is a software that allows the construction and discretization of computational domains for Computational Fluid Dynamics (CFD) and other scientific applications, while the FLUENT software is a commercial code dedicated to the numerical solution of CFD problems. The CFD can be defined as the analysis of systems involving fluid flow, heat transfer and associated phenomena such as chemical reactions by means of computer-based simulation. The technique is very powerful and spans a wide range of industrial and non-industrial application areas. Some example are: turbomachinery, aerodynamics of aircraft and vehicles, hydrodynamics of ships, power plant, electrical and electronic engineering, chemical process engineering, external and internal environment of buildings, marine engineering, environmental engineering, hydrology and oceanography, meteorology, biomedical engineering (Versteeg and Malalasekera, 2007). It is worth to mention that the investment costs of a CFD capability are not small, but the total expense is not normally as great as that of a high-quality experimental facility. Moreover, there are several unique advantages of CFD over 78 Marine Systems & Ocean Technology Vol. 9 No. 2 pp December 2014

9 Computational modeling applied to the study of wave energy converters (WEC) Flávio Medeiros Seibt, Max Letzow, Mateus das Neves Gomes, Jeferson Avila Souza, Luiz Alberto O. Rocha, Elizaldo Domingues dos Santos and Liércio André Isoldi experiment-based approaches to fluid systems design: substantial reduction of lead times and costs of new designs, ability to study systems where controlled experiments are difficult or impossible to perform (e.g. very large systems), ability to study systems under hazardous conditions at and beyond their normal performance limits (e.g. safety studies and accident scenarios), and practically unlimited level of detail of results. The variable cost of an experiment, in terms of facility hire and/or person-hour costs, is proportional to the number of data points and the number of configurations tested. In contrast, CFD codes can produce extremely large volumes of results at virtually no added expense, and it is very cheap to perform parametric studies, for instance to optimize system performance (Versteeg and Malalasekera, 2007). The CFD codes are structured around the numerical algorithms that can tackle fluid flow problems. In order to provide easy access to their solving power all commercial CFD packages include sophisticated user interfaces to input problem parameters and to examine the results. Hence all codes contain three main elements: a pre-processor - that consists in the definition of the geometry of the region of interest (computational domain), the sub-division of this domain into a number of smaller cells (grid generation), the selection of the physical and chemical phenomena that need to be simulated, the definition of fluid properties and the specification of appropriate boundary conditions and initial conditions of the problem; a solver - where occur the Integration of the governing equations of fluid flow over all the cells of the domain, the conversion of the resulting integral equations into a system of algebraic equations (by a discretization method), and the solution of these algebraic equations by an iterative method; a post-processor - is the final step of the numerical simulation, being the CFD packages equipped with versatile data visualization tools which allow a complete analyses of the results (Versteeg and Malalasekera, 2007). The discretization method adopted by the FLUENT software is the Finite Volume Method (FVM). The FVM is well suited for the numerical simulation of various types (elliptic, parabolic or hyperbolic, for instance) of conservation laws. It has been extensively used in several engineering fields, such as fluid mechanics, heat and mass transfer. The FVM can be used on arbitrary geometries, using structured or unstructured meshes, leading to robust schemes. An additional feature is the local conservation of the numerical fluxes, i.e., the numerical flux is conserved from one discretization cell to its neighbor. This last feature makes the FVM quite attractive when modeling problems for which the flux is of importance, such as in fluid mechanics, semi-conductor device simulation, heat and mass transfer. The FVM is locally conservative because it is based on a balance approach: a local balance is written on each discretization cell which is often called control volume; by the divergence formula, an integral formulation of the fluxes over the boundary of the control volume is then obtained, being the fluxes on the boundary discretized with respect to the discrete unknowns (Eymard et al., 2003). So, as already mentioned, in this work the GAMBIT software was employed during pre-processor stage (geometry creation and discretization) and the FLUENT software was used for pre-processing (boundary conditions, models and physical properties setting), solution and post processing of the results. The computational domain is composed by a wave tank in which the converter is assemble. Besides, to obtain a more realistic interaction among water, air and converter the multiphase Volume of Fluid (VOF) model is adopted (Hirt and Nichols, 1981). The VOF is a multiphase model used to solve fluid flow problems with two or more immiscible fluids. In this formulation, all phases are well defined and the volume occupied by one phase cannot be occupied by the other. Thus, to represent these phases inside of each control volume is necessary to consider the volume fraction () concept. Hence it is necessary that the sum of all phases for each cell be always equal to one. In this work there are only two phases: water and air. Therefore if = 1 the cell is full of water; if = 0 the cell is without water, i.e., it is filled of air; and if the value of is between 0 and 1 the cell contain the interface between water and air (Srinivasan et al., 2011). Moreover, when the VOF method is used a single set of momentum and continuity equations is applied to all fluids, and the volume fraction of each fluid in every computational cell (control volume) is tracked throughout the domain by the addition of a transport equation for the volume fraction. Thus, the model is composed by the continuity equation (FLUENT, 2007; Grimmler et al., 2012): v 0 t the volume fraction equation, v 0 t and momentum equations, t v vv p g being: the fluid density, t the time, the flow velocity vector, p is the static pressure, the molecular viscosity, the stress tensor and g the gravitational acceleration. As a single set of momentum and continuity equations is solved for both phases it is necessary to evaluate average values for density and viscosity, respectively (Srinivasan et al., 2011): 1 (4) water air 1 (5) water air Besides, to generate regular waves in the wave tank (representing the incident ocean waves to the OWC converter) (1) (2) (3) Vol. 9 No. 2 pp December 2014 Marine Systems & Ocean Technology 79

10 Computational modeling applied to the study of wave energy converters (WEC) Flávio Medeiros Seibt, Max Letzow, Mateus das Neves Gomes, Jeferson Avila Souza, Luiz Alberto O. Rocha, Elizaldo Domingues dos Santos and Liércio André Isoldi the components of wave velocity in the longitudinal and vertical directions, based on the Stokes Second Order Theory, are used and defined, respectively, by (Dean and Darlymple, 1991): Hgk cosh k h z u cos kx t 2 cosh kh 2 3H k cosh 2k h z cos 4 kx t (6) 16 senh kh And Hgk senh k h z w sen kx t 2 cosh kh 2 3H k senh 2k h z sen 4 kx t (7) 16 senh kh where: H is the wave height, k 2 L is the wave number, h is the water depth into the wave tank, 2 T is the angular frequency, x and z represent the longitudinal and vertical directions, respectively, L is the wave length and T is the wave period. These components of wave velocity are applied as boundary conditions in the left side of the computational domain with the purpose to mimic the effect of the wavemaker at the channel inlet. The other boundary conditions applied are the no slip condition in bottom and in the write wall of the wave tank, and the prescribed atmospheric pressure in the top and in the segment above the wavemaker. The solver is pressure-based, employing upwind and PRESTO for spatial discretizations of momentum and pressure, respectively. The velocity-pressure coupling is performed by the PISO algorithm, while the GEO-RECONSTRUCTION method is employed to tackle with the volume fraction. Moreover, under-relaxation factors of 0.3 and 0.7 are imposed for the conservation equations of continuity and momentum, respectively. It is important to highlight that this numerical model, for the wave generation into a wave tank, was already verified and validated in Gomes et al. (2009) and in Seibt et al. (2014). 3 Wave energy converters (WEC) There is a great diversity of equipment prototype to convert the sea wave energy into electrical energy. The most common classification of these devices is related with the water depth where occurs its installation, considering three groups: onshore devices (with access by land), nearshore devices (at depths between 8 and 25 m) and offshore (at depths greater than 25 m). Other possible classification is related with the way of the wave energy is converted into electricity, i.e., related with the converter operating principle. In accordance with this classification there are fundamentally three main classes: the Oscillating Water Column (OWC), the Floating Bodies (point absorbers or surging devices) and the Overtopping devices (Cruz and Sarmento, 2004). This classification does not include all types of converters, as is the case of the Submerged Plate device. So, among the several types of WEC, this work deals with the operational principle of the OWC, Overtopping and Submerged Plate devices. For this reason, hereafter a brief explanation about each of these converters is made, aiming to facilitate the comprehension of the results generated with the presented computational model. 3.1 Oscillating water column (OWC) An Oscillating Water Column (OWC) converter is a steel or concrete structure with a chamber presenting at least two openings, one in communication with the sea and one with the atmosphere (Fig. 1). Under the action of waves the free surface inside the chamber oscillates and displaces the air above the free surface. The air is thus forced to flow through a turbine that generates electrical power (Nielsen et al., 2006). Usually a Wells turbine is employed; such turbines, once started, turn in the same direction to extract power from air flowing in either axial direction, i.e., the turbine motion is independent of the fluid direction (Twidell and Weir, 2006). Fig. 1 Schematic representation of an Oscillating Water Column (OWC) converter. The greatest disadvantage of the OWC converter is the large dimensions of the structure. As a result, the cost of a single device is rather high (Khaligh and Onar, 2010). An advantage of using the OWC device for power extraction is that the air speed is increased by reduction in the cross-sectional area of the channel approaching the turbine. This couples the slow motion of the waves to the fast rotation of the turbine without mechanical gearing (Twidell and Weir, 2006). Another important advantage is that the moving mechanical parts, that is, the turbine and the generator, are not in direct contact with sea water (Khaligh and Onar, 2010). 3.2 Overtopping The Overtopping device consists of a ramp that captures the water close to the wave crest and introduces it, by over spilling, into a reservoir where it is stored at a level higher than the average free-surface level of the surrounding sea (Fig. 80 Marine Systems & Ocean Technology Vol. 9 No. 2 pp December 2014

11 Computational modeling applied to the study of wave energy converters (WEC) Flávio Medeiros Seibt, Max Letzow, Mateus das Neves Gomes, Jeferson Avila Souza, Luiz Alberto O. Rocha, Elizaldo Domingues dos Santos and Liércio André Isoldi 2). The potential energy of water trapped in the reservoir is then converted into electrical energy through a low head turbine connected to a generator (Dos Santos et al., 2013). average parameters of this wave are: T = 10 s, H = 1.5 m, L = 109 m and h = 15 m, representing the average wave that occurs in the coast of city of Rio Grande (in extreme southern of Brazil). The 2D computational domain, which was discretized with a regular mesh composed by quadrilateral cells with characteristic length of 0.2 m, can be viewed in Fig. 4. The time step used in this numerical simulation was s. Fig. 2 Sketch of the Overtopping device. 3.3 Submerged plate The Submerged Plate is a horizontal structure commonly used in coastal engineering applications (Brossard et al, 2009). One of these applications is its use as a WEC, harnessing the movement of water circulation below the plate which is generated when the ocean waves pass above the plate (Carter, 2005). As indicated in Fig. 3, the water axial velocity below the device occurs in an alternate way, being this alternate water flow responsible to drive a hydraulic turbine installed bellow the plate. As in the OWC converter a turbine needs to keep the same rotation direction independently of the flow direction (Orer and Ozdamar, 2007). The Submerged Plate has some advantages when compared with other wave energy converters, e.g., the device works submerged (which leads to a lower mechanical effort caused by the wave impact and lower maintenance costs since turbine materials have lower corrosion). Moreover, the system can be used for two functions simultaneously: breakwater and energy converter and has a reduced influence over the environment (Seibt et al, 2012). Fig. 4 Computational domain of the OWC device (Gomes, 2010). In Fig. 5 the fluid-dynamic behavior inside the hydropneumatic chamber of the OWC converter is showed during the compression (Figs. 5(a) and 5(b)) and decompression (Figs. 5(c) and 5(d)) of the air. One can note in Fig. 5(a) when the wave crest (in red) reaches the OWC converter, the air (in blue) is compressed inside the chamber and forced to flow out the device through the chimney. This behavior can be visualized in Fig. 5(b) where the vertical velocity of the air flow is positive. On the other hand, in Fig. 5(c) a wave trough is reaching the OWC, generating a decompression inside the hydro-pneumatic chamber. Hence the external air enters through the chimney into the converter, originating an air flow with a negative vertical velocity, as can be seen in Fig. 5(c). Fig. 3 Illustration of the Submerged Plate device. 4 Results and discussion To demonstrate the potentiality of the computational modeling application in the analyses of WEC, case studies about the operational principle of an OWC, Overtopping and Submerged Plate devices were addressed in this work. 4.1 OWC converter An onshore OWC converter submitted to the incidence of regular waves with real characteristics was considered. The Fig. 5. Detail of the hydro-pneumatic chamber of the OWC device (Gomes, 2010). Vol. 9 No. 2 pp December 2014 Marine Systems & Ocean Technology 81

12 Computational modeling applied to the study of wave energy converters (WEC) Flávio Medeiros Seibt, Max Letzow, Mateus das Neves Gomes, Jeferson Avila Souza, Luiz Alberto O. Rocha, Elizaldo Domingues dos Santos and Liércio André Isoldi 4.2 Overtopping converter In this section a 3D numerical investigation about an Overtopping device in laboratory scale is presented. The computational domain is indicated in Fig. 6 and it was subdivided in three regions to obtain the spatial discretization. The first region, upstream of the device (0 m x 2.4 m), and the third region, downstream of the device (3.2 m x 6 m), it were discretized with a regular mesh generated by hexahedral cells with characteristic length of 0.2 m; while the second region, defined where the converter is placed (2.4 m x 3.2 m), it was discretized by tetrahedral cells, with characteristic length of 0.2 m, due its geometry complexity. The temporal discretization was made with a time step of s. Fig. 7. Numerical results for the incidence of waves over the Overtopping device: (a) t = 1 s; (b) t = 2 s; (c) t = 3 s; (d) t = 4 s; (e) t = 5 s; (f) t = 6 s; (g) t = 7 s; and (h) t = 8 s (Machado et al., 2011). Fig. 6. Computational domain of the Overtopping device (Machado et al., 2011). Regular waves, in a laboratory scale, were generated with the follow characteristics: T = 0.88 s, H = 0.18 m, L = 1.2 m and h = 0.6 m. In Fig. 7 it is depicted the transient behavior of the waves generation and its incidence over the Overtopping converter. Fig. 8. Computational domain of the Submerged Plate device. It is possible to notice in Fig. 7 the interaction among water (blue), air (red) and converter (black). Moreover, the interface between water and air (green) can also be observed. These images were obtained from a x-z plane located at the middle of the wave tank (y = 0.5 m). For the time t = 1 s, the formation of the first wave can be viewed in Fig. 7(a). After that, for t = 3 s, this first wave reaches the Overtopping device, as can be seen in Fig. 7(c). So, in Fig. 7(e) for t = 5 s, the wave overcomes the ramp and consequently the water enters into the reservoir. Finally, for t = 8 s in Fig. 7(h), the amount of water that not overtopped the ramp returns to the wave tank. Regular waves, with T = 1.5 s, H = 0.06 m, L = 3 m and h = 0.6 m, were generated in the wave tank. The incidence of these waves over the horizontal plate, placed in the middle of the wave tank at a height of H p = 0.52 m, promotes an alternate water flow bellow the plate that was monitored at the point p (see Fig 8.). Its numerical sensor recorded the transient behavior of the horizontal velocity of the water flow, as can be seen in Fig Submerged plate converter A 2D approach was adopted to numerically study the operational principle of a Submerged Plate (Seibt et al. 2013b). Its computational domain is showed in Fig. 8 and it was discretized by a mesh of quadrilateral cells with characteristic length of 0.01 m. Besides, a time step of s was used to the time discretization. Fig. 9. Transient velocity variation below the Submerged Plate converter (Seibt et al., 2012). 82 Marine Systems & Ocean Technology Vol. 9 No. 2 pp December 2014

13 Computational modeling applied to the study of wave energy converters (WEC) Flávio Medeiros Seibt, Max Letzow, Mateus das Neves Gomes, Jeferson Avila Souza, Luiz Alberto O. Rocha, Elizaldo Domingues dos Santos and Liércio André Isoldi One can observe in Fig. 9 the variation of the water flow horizontal velocity below the plate, alternating positive and negative values. This behavior is in accordance with previous description presented in the literature (see Seibt et al. 2014). As the flow starts from rest at t = 0 s due to its inertia only after approximately 9 s the flow velocity in horizontal direction begins its alternate movement below the plate. In addition, Fig. 9 indicates that the higher magnitudes for the horizontal velocity are obtained in opposite direction to the wave propagation direction, being this trend already observed in other researches, as in: Carter (2005), Orer and Ozdamar (2007) and Seibt et al. (2013). Therefore, one can note the potentiality of the computational modeling application to the study of the WECs, allowing to simulate its fluid-dynamic behaviors in a reliable way. Moreover, by means of the numerical simulation it is possible the development of new type of converters as well as the improvement of the knowledge about the existing ones. Other important aspect that can be highlighted with the use of computational models is the search of geometries for the WECs that leads a superior performance, i.e., the combined use of a geometric optimization technique with the numerical simulation. 5 Conclusions This paper presented a computational modeling dedicated to the analysis of the Wave Energy Converters (WEC), which are responsible to convert the ocean wave energy into electrical energy. By means the numerical simulation it is possible to reproduce adequately and accurately the operating principle of the studied WEC, as well as, obtain future theoretical recommendations for design of these devices. To demonstrate the applicability of the proposed computational model three converters with different operating principles were numerically studied. It is worth to mention that this model was verified and validated previously in the works of Gomes et al. (2009) and Seibt et al. (2014). In the first case study an OWC device with real dimensions was analyzed by a 2D numerical simulation. It was possible to observe the incidence of the waves on the converter, promoting a piston-type movement inside the hydropneumatic chamber. Hence, when the wave crest reaches the OWC a compression occurs, as well as, if a wave through is on the OWC an internal decompression is generated. So, due to the oscillating movement of the wave column inside the chamber, an alternate air flux can be noted at the chimney region, being this flow responsible to drive a turbine which allows the conversion of the sea waves energy into electricity. After that, a 3D numerical approach was used to study an Overtopping converter in a laboratory scale. It was possible to observe the transient behavior of the waves, from its generation until reaches the device. Besides, it was possible to reproduce the complex interaction between water/air flow and the converter ramp. If the incident waves have sufficient amount of energy to overtop the ramp, the water enters into the reservoir and it is used to drive a turbine to generate electrical energy from the sea wave energy. Finally the Submerged Plate converter was analyzed by a 2D numerical simulation, also in laboratory scale. The incidence of the waves on the device promotes an alternate water flux over the plate, which was proved by the periodic variation of its horizontal velocity value. This water movement can be harnessing to convert the waves energy into electrical energy, driving a turbine adequately installed over the plate. Acknowledgements E. D. dos Santos thanks FAPERGS by financial support (Process: 12/1418-4). L. A. O. Rocha and J. A. Souza thanks CNPq by research grant. F. M. Seibt and M. Letzow thanks CAPES by scholarships. References BROSSARD, J., Perret, G., Blonce, L. and Diedhiou, A., (2009) - "Higher harmonics induced by a submerged horizontal plate and a submerged rectangular step in a wave flume". Coastal Engineering, v. 56, n. 1, pp CARTER, W. R., (2005) - "Wave energy converters and a submerged horizontal plate". Thesis of Degree of Master of Science in Ocean and Resources Engineering, University of Hawaii, USA, 273 p. CRUZ, J. M. B. P. and Sarmento, A. J. N. A., (2004) - "Energia das Ondas: Introdução aos Aspectos Tecnológicos, Econômicos e Ambientais". Alfragide: Instituto do Ambiente. Dean, R. G. and Dalrymple, R. A., (1991) - "Water Wave Mechanics for Engineers and Scientists". v. 2, World Scientific. DEVLOO, P. R. B., (2005) - "Simulação numérica". MultiCiência: A Linguagem da Ciência, n. 4, pp DOS SANTOS, E. D., Machado, B. N., Lopes, N., Souza, J. A., Teixeira, P. R. F., Gomes, M. N., Isoldi, L. A. and Rocha, L. A. O., (2013) - "Constructal Design of Wave Energy Converters". In: Rocha, L. A. O., Lorente, S. and Bejan, A. - "Constructal Law and the Unifying Principle of Design". Springer. EYMARD, R. Gallouët T. and Herbin, R., (1997) - "Finite Volume Methods". Handbook of Numerical Analysis, v. 7, pp FERZIGER, J. H. and Peric, M., (1997) - "Computational Methods for Fluid Dynamics". Springer, p Vol. 9 No. 2 pp December 2014 Marine Systems & Ocean Technology 83

14 Computational modeling applied to the study of wave energy converters (WEC) Flávio Medeiros Seibt, Max Letzow, Mateus das Neves Gomes, Jeferson Avila Souza, Luiz Alberto O. Rocha, Elizaldo Domingues dos Santos and Liércio André Isoldi FLUENT, (2007) - "User's Manual". ANSYS, Inc. GOMES, M. das N., (2010) - "Modelagem Computacional de um Dispositivo Coluna d'água Oscilante de Conversão de Energia das Ondas do Mar em Energia Elétrica". Thesis of Degree of Master in Computational Modeling, Federal University of Rio Grande, Brazil, 187 p. GOMES, M. das N., Olinto, C. R., Rocha, L. A. O., Souza, J. A. and Isoldi, L. A., (2009) - "Computational modeling of a regular wave tank". Engenharia Térmica, v. 8, pp GRIMMLER, J. do A. M., Gomes, M. das N., Souza, J. A., dos Santos, E. D., Rocha, L. A. O. and Isoldi, L. A., (2012) - "Constructal Design of a Three-Dimensional Oscillating Water Column (OWC) Wave Energy Converter (WEC)". International Journal of Advanced Renewable Energy Research, v. 1, n. 9, pp HIRT, C. W. and Nichols, B. D., (1981) - "Volume of fluid (VOF) method for the dynamics of free boundaries". Journal of Computational Physics, v. 39, n. 1, pp KHALIGH, A. and Onar, O. C., (2010) - "Energy Harvesting: Solar, Wind, and Ocean Energy Conversion Systems". CRC Press, 341 p. MACHADO, B. N., Zanella, M. M., Gomes, M. das N., Souza, J. A., Dos Santos, E. D., Isoldi, L. A. and Rocha, L. A. O., (2011) - "Numerical Analysis of the Ramp Shape Influence in an Overtopping Converter". In: Ibero Latin American Congress on Computational Methods in Engineering (CILAMCE), UFOP, p MALISKA, C. R., (2004) - "Transferência de Calor e Mecânica dos Fluidos Computacional". LTC - Livros Técnicos e Científicos, p NIELSEN F. G., Andersen M., Argyriadis K., Butterfield S., Fonseca N., Kuroiwa T., Boulluec M. L., Liao S-J., Turnock S. R. and Waegter J., (2006) - "Ocean wind and wave energy utilization". ISSC. ORER, G. and Ozdamar, A., (2007) - "An experimental study on the efficiency of the submerged plate wave energy converter". Renewable Energy, v. 32, n. 8, pp PACHECO, F., (2006) - "Energias renováveis, breves conceitos. Conjuntura e Planejamento". SEI, n. 149, pp TWIDELL, J. and Weir, T., (2006) - "Renewable Energy Resources". 2. ed., Taylor & Francis, 607 p. VERSTEEG, H. K., and Malalasekera, W., (2007) - "An Introduction to Computational Fluid Dynamics". 2. ed., Pearson, p SEIBT, F. M., Couto, E. C., Santos, E. D. dos, Isoldi, L. A., Rocha, L. A. O. and Teixeira, P. R. de F., (2014) - "Numerical Study on the Effect of Submerged Depth on Horizontal Plate Wave Energy Converter". China Ocean Engineering (in press). SEIBT, F. M., Couto, E. C., Santos, E. D. dos, Teixeira, P. R. de F. and Isoldi, L. A., Rocha, (2012) - "Estudo Numérico de uma Placa Submersa Vista como Quebra-Mar e Conversor de Energia das Ondas". In: Seminário e Workshop em Engenharia Oceânica (SEMENGO), FURG, pp SEIBT, F. M., Letzow, M., Vasconcellos, L. da S., Gomes, M. das N., Souza, J. A., Rocha, L. A. O., Santos E. D. dos and Isoldi, L. A., (2013) - "Simulação Numérica Aplicada ao Estudo de Conversores de Energia das Ondas do Mar em Energia Elétrica". In: Conferência Internacional em Tecnologias Naval e Offshore: Energia e Sustentabilidade (NAVTEC), FURG, pp SRINIVASAN, V., Salazar, A. J. and Saito, K., (2011) - "Modeling the disintegration of modulated liquid jets using volume-of-fluid (VOF) methodology". Applied Mathematical Modeling, v. 35, n. 8, pp Marine Systems & Ocean Technology Vol. 9 No. 2 pp December 2014

15 Numerical analysis of an oscillating water column converter considering a physical constraint in the chimney outlet Mateus das Neves Gomes 1,2,*, Flávio Medeiros Seibt 3, Luiz Alberto Oliveira Rocha 2,3,4, Elizaldo Domingues dos Santos 3,4 and Liércio André Isoldi 3,4 1 Instituto Federal de Educação, Ciência e Tecnologia do Paraná (IFPR) 2 Programa de Pós-Graduação em Engenharia Mecânica (PROMEC) - Universidade Federal do Rio Grande do Sul (UFRGS) 3 Programa de Pós-Graduação em Engenharia Oceânica (PPGEO) - Escola de Engenharia (EE), Universidade Federal do Rio Grande (FURG), Av. Itália km 8, CEP , Rio Grande-RS, Brazil. 4 Programa de Pós-Graduação em Modelagem Computacional (PPGMC) - Escola de Engenharia (EE), Universidade Federal do Rio Grande (FURG), Av. Itália km 8, CEP , Rio Grande-RS, Brazil. * Corresponding Author: mateus.gomes@ifpr.edu.br Abstract This work presents a 2D numerical study of an Oscillating Water Column (OWC) converter considering physical constraints in its outlet chimney to represent the turbine pressure drop. Two strategies were adopted. The first considers different dimensions for a physical constraint similar to an orifice plate, being the analysis performed in a laboratory scale. After that, other physical restriction with geometry similar to a rotor turbine was investigated in a real scale by means a dimensional variation. The numerical results indicate the importance of consider the pressure drop caused by turbine in the analysis of the OWC behavior. Keywords Wave Energy, Oscillating Water Column (OWC), Volume of Fluid (VOF), Pressure drop, Turbine. Nomenclature C T Wave tank length N Turbine rotation speed d Physical constraint length T Wave period d 1 Physical constraint diameter t Time g Gravitational acceleration Velocity vector H Wave height x Horizontal direction H T Wave tank height y Normal direction to the x-z plane H 1 OWC chamber height z Vertical direction H 2 OWC chimney height Volume fraction H 3 Lip submergence λ Wave length h Water depth Viscosity L OWC chamber length π Mathematical constant l Chimney outlet diameter Density p Static pressure Stress tensor Vol. 9 No. 2 pp December 2014 Marine Systems & Ocean Technology 85

16 Numerical analysis of an oscillating water column converter considering a physical constraint in the chimney outlet Mateus das Neves Gomes, Flávio Medeiros Seibt, Luiz Alberto Oliveira Rocha, Elizaldo Domingues dos Santos and Liércio André Isoldi 1 Introduction Nowadays the countries are investing in the exploration of new energy sources, especially in those called renewable energy sources. Among several ways to obtain energy from renewable sources, the conversion of the ocean waves energy into electrical one can be an attractive alternative for countries with large coastal regions such as Brazil. The wave power is proportional to its squared amplitude and its period, so waves with high amplitude (around 2 m) and high periods (between 7 and 10 s) normally exceed 50 kw per meter of wave front (Cruz and Sarmento, 2004). The criterion used to classify the Wave Energy Converters (WEC), in most references, is associated with the installation depth of the device. In this context, the WEC are classified in: Onshore devices (with access by earth), Nearshore devices (in depths between 8 and 20 m), and Offshore devices (in depths higher than 20 m). Other possible classification is related with the main operational principle of the wave energy converters, i.e., the converters type. The principal converter types are: Oscillating Water Column (OWC) devices, Floating Bodies devices, and Overtopping devices (Cruz and Sarmento, 2004 In the present work the main operational principle of OWC converters is numerically studied. The purpose here is to consider in the computational model a physical constraint in the chimney outlet mimicking the effect of the turbine over the fluid-dynamic behavior of the OWC chamber, allowing future investigations about the influence of the turbine over the design of the OWC chamber. An analogous approach was already employed by Liu et. al (2009). The computational domains, composed by the OWC inserted into a wave tank, were generated in GAMBIT software. The numerical simulations were performed in FLUENT software, which is a Computational Fluid Dynamic (CFD) package based on the Finite Volume Method (FVM). More details about the FVM can be found in Versteeg and Malalasekera (2007). The Volume of Fluid (VOF) multiphase model was adopted to treat adequately the water-air interaction. The VOF model was developed by Hirt and Nichols (1981) and it was already used in other numerical studies related with wave energy, e.g., Horko (2007), Liu et. al (2008a), Liu et. al (2008b), Gomes (2010), Ramalhais (2011), Liu et. al (2011) and Dos Santos et al. (2013). Besides, regular waves are generated in the wave tank, reaching the OWC converter and generating an alternate air flow through its chimney. Therefore, to study the influence of the pressure drop imposed by the turbine in the OWC fluid-dynamic behavior two different strategies were adopted. Firstly, adopting regular waves in laboratory scale, a restriction similar to a orifice plate was considered in the outlet of the OWC chimney causing a physical constraint in the air flow that cross the chimney. Six dimensions for the opening were tested, allowing the achievement of a curve generated by the relation between two non dimensional parameters: pressure drop and flow coefficients. Other authors also studied these coefficients, as Weber and Thomas (2001), Ramalhais (2011) and Carija et al. (2012). Afterwards, the second strategy also uses a physical constraint, however in this case the constraint is positioned in a way that causes a peripheral air flow in the chimney outlet. Several dimensions for the physical restriction were investigated for regular waves in real scale. From this analysis, it was possible to identify the best constraint dimension, i.e., the dimension that provides the highest power take-off (PTO) available in the OWC chimney. So, taking into account this best restriction dimension, the OWC was submitted to a real wave spectrum. In the sequence of the paper a brief explanation about the OWC main operational principle is performed, followed by the computational modeling description, information about the physical constrains, results and discussion, and conclusions. 2 Oscillating water column (OWC) An Oscillating Water Column (OWC) device is a steel or concrete structure with a chamber presenting at least two openings, one in communication with the sea and one with the atmosphere (Fig. 1). Under the action of waves the free surface inside the chamber oscillates and displaces the air above the free surface. The air is thus forced to flow through a turbine that generates electrical power (Nielsen et al., 2006). Usually a Wells turbine is employed; such turbines, once started, turn in the same direction to extract power from air flowing in either axial direction, i.e., the turbine motion is independent of the fluid flow direction (Twidell and Weir, 2006). The greatest disadvantage of the OWC converter is the large dimensions of structure. As a result, the cost of a single device is rather high (Khaligh and Onar, 2010). An advantage of using the OWC device for power extraction is that the air speed is increased by reduction in the cross-sectional area of the channel approaching the turbine. This couples the slow motion of the waves to the fast rotation of the turbine without mechanical gearing (Twidell and Weir, 2006). Fig. 1 Oscillating water column (OWC) converter. Another important advantage is that the moving mechanical parts, that is, the turbine and the generator, are not in direct contact with water (Khaligh and Onar, 2010). 86 Marine Systems & Ocean Technology Vol. 9 No. 2 pp December 2014

17 Numerical analysis of an oscillating water column converter considering a physical constraint in the chimney outlet Mateus das Neves Gomes, Flávio Medeiros Seibt, Luiz Alberto Oliveira Rocha, Elizaldo Domingues dos Santos and Liércio André Isoldi Fig. 2 Schematic representation of the 2D computational domain. 3 Computational modeling Starting from the definition of the main wave parameters - period (T), height (H), and water depth (h) - it is possible to determine the length (C T ) and height (H T ) of the wave tank, as can be seen in Fig. 2. In addition, the OWC dimensions in agreement with the characteristics of the incident waves must be defined, completing the computational domain geometry (Fig. 2). represent the pressure drop caused by a turbine. The orifice plate was inserted for all cases in the middle of the chimney (H 2 /2). Thus, it is possible to evaluate the effects caused by the presence of a turbine in the fluid-dynamic behavior of the OWC converter. Six different values for the physical constraint were tested, as showed in Fig. 3. Thus, to apply the first proposed strategy (similar to an orifice plate) to investigate the pressure drop imposed to the OWC converter by the turbine, wave parameters and the wave tank dimensions in a laboratory scale are presented in Tab. 1. Table 1. Wave characteristics and dimensions of the tank in laboratory scale. Characteristic Value Fig. 3 Dimensions for the physical constraint represented by an orifice plate. Wave period (T) Wave height (H) Wavelength (λ) Water depth (h) Length of wave tank (C T ) Height of wave tank (H T ) Submergence of OWC (H 3 ) 0.80 s 0.14 m 1.00 m 0.50 m 5.00 m 0.80 m m The other dimensions need to complete the computational domain geometry in this first analysis are indicated in Fig. 2 and their values were defined according with the optimal geometry found in Gomes et al. (2012), being: L = m, l = m, H 1 = m, H 2 = m, H 3 = m, H 2 /l = 3.0, and H 1 /L = As already mentioned, a physical restriction similar to an orifice plate is inserted on the outlet OWC chimney, aiming to The second strategy adopted in this work to reproduce the pressure drop imposed by a turbine in the OWC device also uses a physical restriction, however unlike the orifice plate this constraint promote a peripheral air flow similar to the effect of the flow over a rotor hub (see the geometry in Fig. 4). It is worth to mention that this air flow behavior, flowing peripherally and surrounding the physical restriction, presents a similarity with a real air flow over a turbine. Besides, the use of this geometry in studies concerned with the influence of the turbine in the OWC behavior is an original proposal of the present work. In Fig. 4 it is depicted a sketch indicating the form and location of this physical restriction. The dimensions d and d 1 represents the length and the diameter of the constraint, respectively. Moreover, as a real scale is adopted in this second strategy, the dimensions of the OWC were defined as: L = m, l = m, H 1 = m, H 2 = m, H 3 = 9.50 m, H 1 /L = , H 2 /l = These values correspond to the best shape obtained in Gomes et al. (2013), where a geometric optimization investigation was carried out. Vol. 9 No. 2 pp December 2014 Marine 87Systems & Ocean Technology 87

18 Numerical analysis of an oscillating water column converter considering a physical constraint in the chimney outlet Mateus das Neves Gomes, Flávio Medeiros Seibt, Luiz Alberto Oliveira Rocha, Elizaldo Domingues dos Santos and Liércio André Isoldi Therefore, based on the numerical results generated taking into account the values of Tab. 3, the constraint dimensions that promoted a better harnessing of the incident waves was defined as the optimal geometry of the physical constraint. Thus, this optimal shape was submitted to all waves of the spectrum (Tab. 2). Fig. 4 OWC converter and physical constraint with geometry similar to a turbine in real scale. A real wave spectrum consisting of nine waves was considered here, being the wave and wave tank characteristics indicated in Tab. 2. For all waves of the spectrum (Tab. 2) the following parameters are kept constant: wave height (H) of 1.0 m, water depth (h) of 10.0 m, and tank height (H T ) of 12.0 m. So, taking into account the first wave of the spectrum, i.e., the wave with T = 5.0 s of Tab. 2, the dimensions of the physical constraint were varied as showed in Tab. 3. Highlighting that in these numerical simulations 0 < d 1 < l; and that the d dimension is also variable, being its value obtained by: d = (1 + d 1 /2) m. Table 2 Wave spectrum. Period (T) Wave length (λ) Tank length (C T ) Table s 37.6 m m 6.0 s 48.5 m m 7.0 s 60.0 m m 7.5 s 65.4 m m 8.0 s 71.0 m m 9.0 s 81.8 m m 10.0 s 92.0 m m 11.0 s m m 12.0 s m m Dimensions of the physical constraint. Case Constraint diameter (d 1 ) Constraint length (d) m m m m m m m m m m m m 3.1 Boundary conditions One can note in Fig. 2 that the generation of waves is performed by the imposition of the wave velocities components as boundary conditions (by means of an User Defined Function (UDF) in FLUENT software) in the left side of the computational domain. This numerical methodology to generate regular waves was already verified and validated in Horko (2007), Gomes et al. (2009) and Seibt et al. (2014) and Dos Santos et al. (2013). It is worth to mention that in accordance with Chakrabarti (2005) the wave adopted in the first strategy is classified as a high order wave, while the waves employed for the second strategy are linear waves. The other boundary conditions are the atmospheric pressure in the dashed lines of Fig. 2 and the no slip condition (wall) in the continuous lines of Fig Mathematical model As previously mentioned, the computational domain is composed by a wave tank in which the converter is coupled (Fig. 2). Besides, to obtain a more realistic interaction among water, air and converter the multiphase Volume of Fluid (VOF) model (Hirt and Nichols, 1981) is adopted. The VOF is a multiphase model used to solve fluid flow problems with two or more immiscible fluids. In this formulation, all phases are well defined and the volume occupied by one phase cannot be occupied by the other. Thus, to represent these phases inside of each control volume is necessary to consider the volume fraction () concept. Hence it is necessary that the sum of all phases for each cell be always equal to one. In this work there are only two phases: water and air. Therefore if = 1 the cell is full of water; if = 0 the cell is without water, i.e., it is filled of air; and if the value of is between 0 and 1 the cell contain the interface between water and air (Srinivasan et al., 2011). Moreover, when the VOF method is used a single set of momentum and continuity equations is applied to all fluids, and the volume fraction of each fluid in every computational cell (control volume) is tracked throughout the domain by the addition of a transport equation for the volume fraction. Thus, the model is composed by the continuity equation (FLUENT, 2007; Grimmler et al., 2012): v 0 t (1) 88 Marine Systems & Ocean Technology Vol. 9 No. 2 pp December 2014

19 Numerical analysis of an oscillating water column converter considering a physical constraint in the chimney outlet Mateus das Neves Gomes, Flávio Medeiros Seibt, Luiz Alberto Oliveira Rocha, Elizaldo Domingues dos Santos and Liércio André Isoldi the volume fraction equation v 0 t and momentum equations: t v vv p g (2) (3) being: the fluid density, t the time, the flow velocity vector, p is the static pressure, the molecular viscosity, the stress tensor and g the gravitational acceleration. The momentum and continuity equations are solved for the mixture of both phases (air and water). Then, it is necessary to evaluate average values for density and viscosity, respectively (Srinivasan et al., 2011): water 1 air (4) 1 (5) water air 3.3 Numerical procedures As earlier mentioned, the conservation equations of mass and momentum and the equation for transport of volume fraction are solved with the finite volume method (FVM). The solver is pressure-based, employing upwind and PRESTO for spatial discretizations of momentum and pressure, respectively. The velocity-pressure coupling is performed by the PISO algorithm, while the GEO-RECONSTRUCTION method is employed to tackle with the volumetric fraction. Moreover, under-relaxation factors of 0.3 and 0.7 are imposed for the conservation equations of continuity and momentum, respectively (Gomes et al., 2012). 4 Results and discussion Fig. 5 Pressure inside the OWC chamber as a function of time. Figure 5 indicates that if the physical constraint dimension increases a higher pressure variation is observed. The pressure drop is estimated by the difference between the pressure inside the OWC chamber (which is monitored in several points) and the pressure in the outlet region of the chimney (which is monitored by a sensor placed in this region). Accordingly, non dimensional coefficients related with the pressure and the flow rate in the OWC converter can be evaluated as follow (Carija et al. (2012): p 2 2 (6) N D a. m (7) 3 a N D. where: Δp is the pressure drop, m is the mass flow rate, a is the air density, N is the speed of the turbine rotation, and D is the turbine diameter. Considering average values for the pressure and mass flow rate, which were obtained by application of the Root Mean Square (RMS) technique (Gomes et al., 2012) in the transient numerical results, the pressure drop coefficient is depicted as a function of flow coefficient in Fig Strategy 1 (orifice plate) In this first approach the six dimensions for the physical constraint in the OWC chimney outlet (Fig. 3) were numerically simulated. In all simulations a regular mesh generated by square cells with side of 0.01 m and a time step of s were adopted to reproduce the incidence of eight waves (4.8 s) over the OWC device. During this time of 4.8 s there is no effects caused by the wave reflection since the length of the wave tank is C T = 5.0 m. Besides, the wave propagation is considered stabilized when t 2.4 s, i.e., after the formation of the third wave. The presence of these restrictions promotes a pressure drop in the region where it should be located the turbine as well as a significant increase in the pressure inside the hydro-pneumatic chamber of the OWC, as one can observe in Fig. 5. Fig. 6 Pressure drop coefficient as a function of the flow coeficcient - Strategy 1 (laboratory scale). Vol. 9 No. 2 pp December 2014 Marine 89Systems & Ocean Technology 89

20 Numerical analysis of an oscillating water column converter considering a physical constraint in the chimney outlet Mateus das Neves Gomes, Flávio Medeiros Seibt, Luiz Alberto Oliveira Rocha, Elizaldo Domingues dos Santos and Liércio André Isoldi Figure 6 allows to verify that there is a linear relation adjusted from the obtained points between the pressure drop coefficient and flow coefficient: Φ = KΨ, being K = This type of relation is similar to that found in experimental and numerical works of Wells turbine, see Ramalhais (2011). only the best shape among the above cases was submitted to the wave spectrum indicated in Tab. 2. In these numerical simulations the mesh characteristics and the solution parameters are the same employed in Gomes et. al (2013). After that, it was analyzed the velocity behavior in the region where the physical restriction was placed. As one can note in Fig. 7, the increase of the constraint causes an augmentation in the air flow velocity as well as a higher pressure drop, in a linear behavior. For this relation between velocity and pressure average values were considered, being these values linearly fitted with a maximum error of 4%. In Fig. 8 the velocity behavior inside the OWC device is presented for all studied cases in the instant t = 4.0 s showing that the velocity increases as the constraint increases, especially in the constraint region. It is also noticed a significant modification of the fluid flow inside the chamber. In all simulations the OWC dimensions were kept constant, excepting the constraint dimension which vary for each case. These results obtained with the strategy of reproducing the turbine effect over the OWC air flow by means a physical restriction presented allows its utilization in a satisfactory way, i.e., imposing the pressure drop that would be caused by the turbine. (a) (b) (c) (d) Fig 7 Velocity versus pressure drop. 4.2 Strategy 2 (rotor hub geometry) This second strategy aims to test a physical restriction considering a more realistic geometry (Fig. 2), similar to the rotor hub geometry, in the OWC chimney. Hence, the behavior of the air flow when passing through the turbine and hence the pressure drop will also be more realistic. To do so, it were tested several dimensions for this constraint, as presented in Tab. 3, allowing to assess the relation between flow and pressure drop coefficients which occurs in the turbine of OWC device. As earlier mentioned, it was taken into account an OWC converter with constant dimensions, being only varied the physical constraint diameter, in accordance with Tab. 3 and submitted to the first regular wave of Tab. 2. Posteriorly, (e) Fig 8. Velocity behavior on the instant t = 4.0 s for: (a) case 0, (b) case 1, (c) case 2, (d) case 3, (e) case 4, (f) case 5. As expected, the decrease of the region through which the air flows by the constraint increase makes the internal pressure of the OWC converter also increases and hence occurring a power augmentation, as can be noted in Tab. 4. It is important to mention that the values of Tab. 4 are obtained by the RMS technique, evaluated in the interval time 15 s t 30 s, in which the wave generation is stabilized and there is no influence of wave reflection. In Tab. 4 the mass flow rate average values until case 4 are almost constant, but from case 4 a more significant difference can be observed. As the OWC converter in all six cases is submitted to the incidence of the same regular waves, the mass flow rate should be constant. (f) 90 Marine Systems & Ocean Technology Vol. 9 No. 2 pp December 2014

21 Numerical analysis of an oscillating water column converter considering a physical constraint in the chimney outlet Mateus das Neves Gomes, Flávio Medeiros Seibt, Luiz Alberto Oliveira Rocha, Elizaldo Domingues dos Santos and Liércio André Isoldi Table 4 Results considering the physical restriction diameter (real scale). Physical Restriction Mass flow (kg/s) Pressure drop (Pa) Power (W) , , , However, the variation of this quantity noted in the results of Tab. 4 must be caused by the increasing of the physical restriction, which causes an air flow damping. As a consequence, the pressure and the power also increase as can be seen in Fig. 9. Therefore, the results showed that, among the studied cases, the case 4 as the most appropriate physical restriction. Finally, in Fig. 10, a graph relating the pressure and flow coefficients are obtained from the numerical simulations. One can note a linear trend between these coefficients, which is a typical characteristic of a Wells turbine. So, if a linear fit is applied, as performed in Weber and Thomas (2001), the following relation is obtained: Φ = Ψ, having this value the same order of magnitude of that presented in Weber e Thomas (2001). Table 5 Wave Numerical results form wave spectrum analysis. Volumetric flow rate [m 3 /s] Pressure [Pa] Mass flow rate [Kg/s] Power [W] Fig. 9 Power variation as a function of the physical constraint diameter (rotor hub geometry). Other consideration that can be made to corroborate the choice of case 4 as the best shape is related with the turbine design. If the difference between the chimney outlet length (l) and the physical restriction diameter (d 1 ) of case 4 is evaluated, a gap of 0.8 m is encountered representing a clearance around 35% of the l dimension. So, using the computational domain of case 4 and the wave spectrum presented in Tab. 2, it was possible to investigate the fluid-dynamic behavior of the OWC converter taking into account the pressure drop imposed by the turbine. Here, the average values were also obtained by RMS technique during an interval time of 15 s t 30 s. In Tab. 5 these values are showed, while in Tab. 6 the pressure and flow rate non dimensional coefficients, defined by Eqs. (6) and (7), respectively, are also presented. It is important to mention that in Eqs. (6) and (7) the speed of the turbine rotation was rad/s (1500 RPM), in agreement with Weber and Thomas (2001). Table 5 indicates that the increase of the wave period promotes a reduction in all quantities analyzed, being this trend also observed in Liu (2009). Table 6 Wave Dimensionless pressure and flow coefficients. Flow rate coefficient Φ Pressure coefficient Ψ Fig. 10 Pressure coefficient versus flow rate coeficcient - Strategy 2. Therefore, considering all discussed aspects it is possible to state that the use of a physical restriction to represent the Vol. 9 No. 2 pp December 2014 Marine 91Systems & Ocean Technology 91

22 Numerical analysis of an oscillating water column converter considering a physical constraint in the chimney outlet Mateus das Neves Gomes, Flávio Medeiros Seibt, Luiz Alberto Oliveira Rocha, Elizaldo Domingues dos Santos and Liércio André Isoldi pressure drop imposed by the turbine over the air flow in an OWC converter computational model can be employed in a satisfactory way, especially for consideration of the turbine effect over the fluid flow inside the chamber and for geometry design of the device. 4 Conclusions This work presented two strategies which can be used in the computational modeling of the operating principle of an OWC converter, aiming to impose over the air flow, by means of a physical constraint, the pressure drop that in practice would be generated by the presence of the turbine. In the first strategy a restriction similar to an orifice plate was considered. In the second approach a restriction with a geometry similar to a turbine rotor hub was taking into account. The obtained results, although in an initial stage, are very promising, because it was possible to analyze the fluiddynamic OWC behavior in a more realistic way. The pressure drop caused by the restriction causes velocity and pressure variations in the air flow similar to those noticed in a real OWC converter. The results also showed that the numerical method proposed here led to a behavior of the effect of the flow coefficient over the pressure drop and over the PTO similar to those obtained into archival literature, allowing its future application for achievement of theoretical recommendations concerned with the design of the device. Acknowledgements E. D. dos Santos thanks FAPERGS by financial support (Process: 12/1418-4). L. A. O. Rocha thanks CNPq by research grant. F. M. Seibt thanks CAPES by scholarship. References CHAKRABARTI, S. K., (2005) - "Handbook of offshore engineering". v. 1, Elsevier, Ilinois, USA, 661 p. CRUZ, J. M. B. P. and Sarmento, A. J. N. A., (2004) - "Energia das Ondas: Introdução aos Aspectos Tecnológicos, Econômicos e Ambientais". Alfragide: Instituto do Ambiente. CARIJA, Z., Kranjcevic, Banic,V., Cravak, M., (2012) - "Numerical analysis of wells turbine for wave power conversion". Engineering Review, v. 3, n. 3, pp DOS SANTOS, E. D., Machado, B. N., Lopes, N. R., Souza, J. A., Teixeira, P. R. F., Gomes, M. das N., Isoldi, L. A., Rocha, L. A. O. (2013) - Constructal Design of Wave Energy Converters. In: Rocha, L. A. O., Lorente, S., Bejan, A. (Eds.), Constructal Law and the Unifying Principle of Design, Springer, New York, pp FLUENT, (2007) - "User's Manual". ANSYS, Inc. GOMES, M. das N., Olinto, C. R., Rocha, L. A. O., Souza, J. A. and Isoldi, L. A., (2009) - "Computational modeling of a regular wave tank". Engenharia Térmica, v. 8, pp GOMES, M. das N., (2010) - "Modelagem Computacional de um Dispositivo Coluna d'água Oscilante de Conversão de Energia das Ondas do Mar em Energia Elétrica". Master Thesis in Computational Modeling, Federal University of Rio Grande, Brazil, 187 p. GOMES, M. das N., Nascimento, C. D., Bonafini, B. L., Dos Santos, E. D, Isoldi, L. A. and Rocha, L. A. O., (2012) - "Two-dimensional geometric optimization of an oscillating water column converter in laboratory scale". Engenharia Térmica, v.11, pp GOMES, M. das N., Dos Santos, E. D, Isoldi, L. A. and Rocha, L. A. O., (2013) - "Two-dimensional geometric optimization of an oscillating water column converter of real scale". In: 22 nd International Congress of Mechanical Engineering (COBEM), Ibero Latin American Congress on Computational Methods in Engineering (CILAMCE), pp GRIMMLER, J. do A. M., Gomes, M. das N., Souza, J. A., dos Santos, E. D., Rocha, L. A. O. and Isoldi, L. A., (2012) - "Constructal Design of a Three-Dimensional Oscillating Water Column (OWC) Wave Energy Converter (WEC)". International Journal of Advanced Renewable Energy Research, v. 1, n. 9, pp HIRT, C. W. and Nichols, B. D., (1981) - "Volume of fluid (VOF) method for the dynamics of free boundaries". Journal of Computational Physics, v. 39, n. 1, pp HORKO, M., (2007) - "CFD Optimisation of an Oscillating Water Column Energy Converter". Master Thesis in Engineering ans Science, Scholl of Mechanical Engineering, University of Western, Australia, 145 p. KHALIGH, A. and Onar, O. C., (2010) - "Energy Harvesting: Solar, Wind, and Ocean Energy Conversion Systems". CRC Press, 341 p. LIU, Z.; Hyun B.; Hong, K., (2008a) - "Application of Numerical Wave Tank to OWC Air Chamber for Wave Energy Conversion". International Offshore and Polar Engineering Conference. 92 Marine Systems & Ocean Technology Vol. 9 No. 2 pp December 2014

23 Numerical analysis of an oscillating water column converter considering a physical constraint in the chimney outlet Mateus das Neves Gomes, Flávio Medeiros Seibt, Luiz Alberto Oliveira Rocha, Elizaldo Domingues dos Santos and Liércio André Isoldi LIU, Z.; Hyun B.; Jin, J., (2008b) - "Numerical prediction for overtopping performance of OWEC". Journal of the Korean Society for Marine Environmental Engineering, v. 11, n.1, p LIU, Z. ; Hyun, B. S.; Hong, K. and Lee, Y., (2009) - "Investigation on integrated system of chamber and turbine for OWC wave energy convertor". In: Proceeding of the nineteenth international offshore and polar engineering conference, pp LIU, Z.; Hyun B.; Hong, K., (2011) - "Numerical study of air chamber for oscillating water column wave energy convertor". China Ocean Eng., v. 25, pp NIELSEN F. G., Andersen M., Argyriadis K., Butterfield S., Fonseca N., Kuroiwa T., Boulluec M. L., Liao S-J., Turnock S. R. and Waegter J., (2006) - "Ocean wind and wave energy utilization". ISSC. RAMALHAIS, R. dos S., (2011) - "Estudo numérico de um dispositivo de conversão da energia das ondas do tipo coluna de água oscilante (CAO)". Dissertação (Mestrado em Engenharia Mecânica) - Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa, Lisboa, Portugal, 107 p. SEIBT, F. M., Couto, E. C., Santos, E. D. dos, Isoldi, L. A., Rocha, L. A. O. and Teixeira, P. R. de F., (2013) - "Numerical Study on the Effect of Submerged Depth on Horizontal Plate Wave Energy Converter". China Ocean Engineering (in press). SRINIVASAN, V., Salazar, A. J. and Saito, K., (2011) - "Modeling the disintegration of modulated liquid jets using volume-of-fluid (VOF) methodology". Applied Mathematical Modeling, v. 35, n. 8, pp TWIDELL, J. and Weir, T., (2006) - "Renewable Energy Resources". 2. ed., Taylor & Francis, 607 p. VERSTEEG, H. K., and Malalasekera, W., (2007) - "An Introduction to Computational Fluid Dynamics". 2. ed., Pearson, p WEBER, J. W. and Thomas, G. P., (2001) - An investigation into the importance of the air chamber deign of an oscillating water column wave energy device. In: Proceeding of the eleventh international offshore and polar engineering conference, pp Vol. 9 No. 2 pp December 2014 Marine 93Systems & Ocean Technology 93

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25 Preliminary study about the wave influence on the ship hydrodynamics Amanda Armudi 1, Wiliam C. Marques 2, Jorge F. C dos Santos 2, Lucas S. Bravo 3 and Elisa H. Fernandes 1, Pedro V. Guimarães 1 1 Instituto de Oceanologia, Universidade Federal do Rio Grande, FURG, Rio Grande, Brasil, amandaarmudi@gmail.com 2 Instituto de Matemática, Estatística e Física, Universidade Federal do Rio Grande, FURG, Rio Grande, Brasil 3 Escola de Engenharia, Universidade Federal do Rio Grande, FURG, Rio Grande, Brasil Abstract The computational modeling is an important tool that can be used to assist the development of engineering projects. In this work a two-dimensional numerical model, under development at the Universidade Federal do Rio Grande, is used to describe the ship hydrodynamics (using three degrees of freedom) and understand the behavior under variation of: thrust produced by the engine and effects of external forces, focusing in wave influence. This work is based on the development of the numerical model to investigate the ship hydrodynamics using three degrees of freedom through the Lagrangian Mechanics. The thrust is represented in exponential form increasing or decreasing over 30 hours of numerical simulation, on the other hand, the wave properties are obtained from a numerical model SWAN for the coastal region adjacent to the Patos Lagoon. The vessel velocity is a function of the thrust and for both simulations some variations are observed for the two components during the first hour of simulation. During this period of simulation, the variation of the initial velocity favors the more effective action of inertial forces. After 1 hour of simulation, the thrust and the ship velocity reaches a period of stabilization. During this period, the influence of the external forces associated with the wave and drag effects are observed, in this way the effects of pressure gradients become important causing increasing (reducing) of the ship velocity according with the increasing (reduction) of the wave velocity. On the situation with the thrust decreasing, the variations on the x and y components are not observed. On the other hand, for the situation with the increasing thrust the variations on the x and y components reflect on lateral deviations of the ship trajectory. Keywords: numerical modeling; vessel; thrust Nomenclature X vessel s translation u vessel s acceleration R(θ) vessel s rotation u vessel s velocity C(t) vessel s contour E increasing thrust L Lagrangian of the sistem E d decreasing thrust T kinetic energy ρ fluid density U potential energy D transversal ship dimension x, y and θ generalized coordinates A ship area x, y and θ temporal variation hw significant wave height m mass C D drag coefficient I inertia matrix C M inertial coefficient MA additional mass matrix v n velocity of the fluid B potential damping matrix v n acceleration of the fluid F c Coriolis Centrifuge effort h integration step applied E engine thrust n number of iterations counted F EXT external forces Vol. 9 No. 2 pp December 2014 Marine Systems & Ocean Technology 95

26 Preliminary study about the wave influence on the ship hydrodynamics Amanda Armudi, Wiliam C. Marques, Jorge F. C dos Santos, Lucas S. Bravo, Elisa H. Fernandes and Pedro V. Guimarães 1 Introduction The computational modeling is used in order to simulate natural physical process, as well as, an auxiliary tool applied during the development of engineering projects. The use of numerical simulations reduces the costs related to smaller scale processes and the risks of hydro-mechanical accidents. For instance, during certain project stages of: ship construction and ship displacement at sea. The numerical model can avoid or minimize accidents at estuarine regions and coastal seas during normal and hazardous conditions, as storms with high wave action and strong winds. Through the simulation is possible understand the ship behavior during these conditions and thus predict what are the ideal conditions for the ship navigability. According to Sclavonous (1984), the evolution of the offshore sector demanded the development of new configurations with operation of advance speed ships. This author investigated the case of the articulate oceanic convoys, approaching operations, offloading and side by side of the oil tankers ship, as well as, the fuel supply entering military ships. 1.1 Background Linear and nonlinear theories of ship wave resistance and motions have been developed over the years, seeking a better form to represent the vessel in the ocean. Kelvin (1887) studied the wave pattern created by the disturbance of moving pressure above the free surface (Yang, 2004). Michell (1898) contributed to develop the hydrodynamic theory (Thin Ship Theory) that was implemented to represent the wave resistance of ships. This approximation had a premise of the small beam compared with length ratio and immersion. Therefore, geometric restrictions were considered aiming to solve the problem of boundary conditions using the free surface, on which the boundary condition occurred on the median line of the ship. This theory had a which, and results are not quite similar to the experiments data. In this way, this theory is not used in naval architecture. The Strip Theory was the first method convenient for numerical computations developed by Korvin-Kroukovsky and Jacobs (1955). In the strip theory, the three-dimensional problem is reduced to some two-dimensional problems, because the length ship is divided on transverse sections, and the flux acts in each section with vertical and transversal directions. The ship used by this theory is slender with low advance speed and influenced by the short wave length when compared with the vessel length. This theory produces good results for the pitch and heave movements. The Slender Body Theory consider the three-dimensional slender bodies of aerodynamic theory and to hydrodynamics. The slender body of ship has the length with the same order of wave length, and the ship needs to have moderate advance speed. Maruo (1962) used this theory whit wave resistance, but the results are weak for low Froude s number and moderate for high Froude`s number. Jensen and Pedersen (1979) were responsible for developing the quadratic theory in the frequency domain. These authors developed this theory in order to made calculations of the nonlinear vertical moment induced by the waves. Aiming to improve the problem of the ship hydrodynamics with waves, Bertram (1990) developed the three-dimensional formulation or panel s method. This method considers the threedimensional effects of the hull on the surrounding flux and the speed effects of ship interacting with the flux. Ayaz, Vassalos and Spyrou (2006) developed a study that proposed a new axis system that allows straightforward combination between sea keeping and maneuvering, whilst accounting for extreme motion. The numerical model incorporates non-linear six-degrees-of-freedom coupled motion equation in the time-domain, with no restrictions of motion amplitude. Seo and Kim (2011) developed a study about numerical analysis on ship maneuvering coupled with ship motion in waves. The ship maneuvering problem in waves is solved by using the time-domain ship motion program, called WISH (computer program for nonlinear Wave Induced load and Ship motion analysis), bases on a B-spline Rankine panel method and the program has two main areas are extended, lateral motions and the coupling of seakeeping and maneuvering models. All these theories contributed to evolve the study of the ship hydrodynamics. However, in this work the aim is starting the development of a Lagrangian numerical model to represent the ship hydrodynamics. This preliminary study presents how the ship behaves considering the thrust variation and external forces, focusing on the wave action. 2 Methodology This work is based on the development of the numerical model to investigate the ship hydrodynamics in two dimensions, allowing three degrees of freedom within the Lagrangian Mechanics. There are similar studies, likewise the numerical modeling of nonlinear ship wave interactions, where the hydrodynamics of a seagoing vessel are numerically modeled through the present invention's new calculative methodology, which uniquely combines vessel boundary characteristics and pseudo-spectral environmental characteristics. Solutions are obtained through mutual transformations between the vessel boundary's irregular grid and the environment's regular pseudo-spectral grid (Lin and Kuang, 2010). 2.1 Mathematical description of the model The development of the numerical model used to describe the ship movements over the time uses concepts of Variational Calculus and Lagrangian Mechanics. The mathematical formulation, the numerical model and the boundary conditions are described below. The coordinate system is 96 Marine Systems & Ocean Technology Vol. 9 No. 2 pp December 2014

27 Preliminary study about the wave influence on the ship hydrodynamics Amanda Armudi, Wiliam C. Marques, Jorge F. C dos Santos, Lucas S. Bravo, Elisa H. Fernandes and Pedro V. Guimarães presented in the Figure 1 with the vessel moving in two dimensions. The consideration allows the application of three degrees of freedom (x, y, θ) and the axes (x, y, θ ) are arranged into the non inertial coordinate system. The origin is following the ship gravity center, but this consideration provides some simplifications on the mathematic expressions. The vessel position is described through Equation (1): X = X + R(θ)[C(t) X] (1) The components are represented by: X = x y (2) Lagrangian (L) of the system and it is represented by L(q,q,t). The Lagrangian can be writing as Equation (5): L = T U (5) where: T is the kinetic energy and U is the potential energy of the dynamic system. The first term considers all the contributions for the kinetic energy of the system. On the other hand, the second contribution considers the energy form including effects of the conservative forces. In this study the potential energy is neglected because the model was developed in two dimensions. From the principle of minimum action was obtained a system of differential equations known as Euler-Lagrange equations. A system with n degrees of freedom over a generalized coordinate system (q 1,q 2,...,q n ) can be write on the non-conservative form as Equation (6): cos (θ) R (θ) = sin(θ) sin (θ) cos (θ) (3) d L dt q L = F q (6) C (t) = K(t) W(t) where: X represents the translation, R(θ) the rotation and C(t) the polynomial function that could be used interpolate and parameterize the vessel contour. (4) ext where: F i are external forces applied to the system. The kinetic energy (L) of the system is represented as: L = m (x + y ) 2 Thus, obtaining the time derivative of the vessel position (Equation 1) and substituting on the Equation (7) the Lagrangian of the system are presented as: (7) L = m 2 x + y 2x [dx sin(θ) + dy cos(θ)]θ + 2y [dx cos(θ) dy sin(θ)]θ + [dx + dy ]θ } (8) The system of ordinary differential equations can be constructed for the three degrees of freedom, surge (x), sway (y) and yaw (θ), using: d dt L L x x = F d dt L L y y = F (9) (10) Fig.1 Coordinate system using three degrees of freedom: surge (x), sway (y) and yaw (θ). On the Lagrangian mechanics formulation, each mechanic system is characterized by a defined functional, which depends of the generalized coordinate system (q), their time derivative (q ) and the time (t). This functional is called d dt L L θ θ = F (11) In the first moment the Lagrangian of the system (Equation 8) was derived according to the generalized Vol. 9 No. 2 pp December 2014 Marine Systems & Ocean Technology 97

28 Preliminary study about the wave influence on the ship hydrodynamics Amanda Armudi, Wiliam C. Marques, Jorge F. C dos Santos, Lucas S. Bravo, Elisa H. Fernandes and Pedro V. Guimarães coordinates (x, y and θ), and their temporal variation (x, y and θ ). Thus, the components:, and were derived according to the time. The derived components of the Lagrangian equation and the external forces applied on the ship are combined through the Equations 9, 10 and 11 in order to provide the system of differential equations used to simulate the ship dynamics. The system of differential equations is presented for the three degrees of freedom as: F = mx + 0y mθ [dxsi n(θ) + dyco s(θ)] mθ [dxco s(θ) dysi n(θ)] (12) = M 0 0 M = 0 M M πρb πρa πρ(a b ) 8 (17) The potential damping matrix is presented in simplified form as: B 0 0 B = 0 B 0 (18) 0 0 B F = 0x + my + mθ [dxcos(θ) + dyson(θ)] mθ [dxsin(θ) dycos(θ)] (13) F = mx [dx sin(θ) + dy cos(θ)] + my [dx cos(θ) dy sin(θ)] + mθ [dx + dy ] (14) (13) (14) The Coriolis Centrifuge effort is represented by the matrix (19): m[dxcos(θ) dysin(θ)]θ F = m[dxsin(θ) + dycos(θ)]θ (19) 0 The external forces represented by the wave and drag action are presented by the matrix (Equation 20) and the thrust applied by the ship engine is used as the matrix (Equation 21) F = F F 0 (20) Considering all the external forces applied in this work and performing the algebraic procedure to rearrange the equations, is possible to assemble on the matrix form a system of differential equations that represent the vessel hydrodynamics with three degrees of freedom represented by the Equation (15): (I + MA)u + Bu + F θ, θ = E + F (15) where: I represent inertia matrix (kg), MA the additional mass matrix (kg), B is the potential damping matrix (kg/s), F c is the vector of Coriolis Centrifuge effort, F E is the vector of external forces (N), E is the vector of engine thrust (N), u and u are the acceleration and velocity of the ship (m/s), respectively. The inertia matrix is presented below as: I = m + M 0 m[dxsin(θ) + dycos(θ)] 0 m + M m[dxcos(θ) dysin(θ)] m[dxsin(θ) + dycos(θ)] m[dxcos(θ) dysin(θ)] m[dx + dy ] with, the M matrix represented by: (16) E = E E 0 (21) 2.2 External Forces In 1950 year, Morison proposed one formulation for the calculation of hydrodynamic forces assuming a rigid cylindrical element quiescent, submerged into the fluid with continuous flow at the normal direction to the element axis. Morison s equation considered that the body element dimensions not caused effects on the outflow. Even with these simplifications, the Morison s equation presents good results in practical applications. In this formulation is considered two different contributions, one concerning to the flow drag effect and other relative to inertial forces that arise on the vessel structure. The general equation for the calculation of the hydrodynamic forces is based on the initial formulation proposed by Morison, being composed by three contributions. The first parcel represents the relative drag forces between the fluid and the structure. The second parcel is relative to the acceleration or deceleration of the ship and it has origin in the pressure gradients which arises on the body ship surface. The third 98 Marine Systems & Ocean Technology Vol. 9 No. 2 pp December 2014

29 Preliminary study about the wave influence on the ship hydrodynamics Amanda Armudi, Wiliam C. Marques, Jorge F. C dos Santos, Lucas S. Bravo, Elisa H. Fernandes and Pedro V. Guimarães component represents the relative inertial force corrected by additional mass relative to the wave intensity. k = hf x + h 2, y + k (26) 2 This study used a variation of the Morison s equation (Marques, 2010), where the flow acts on the structure with elliptic geometrical form, which has an arbitrary movement and orientation. In this way, the Morison s equation applied to this study is presented by the Equation (22): F = 1 2 ρc D(v u ) v u ρau hw(c 1) + ρc Av (22) where: ρ is the fluid density, D is a transversal ship dimension, A is the ship area, hw is the significant wave height, C D is the drag coefficient, C M is an inertial coefficient, u n and u nare the velocity and acceleration of the vessel, respectively and v n and v n are the velocity and acceleration of the fluid, respectively. The water density is calculated through the international equation for sea water state, Roy Chester (2002) from real data of temperature and salinity obtained near the Patos Lagoon mouth, located in the southernmost part of the Rio Grande do Sul state, Brazil. The influence of the waves generated by the winds was considered through the using of significant wave height, velocity of the phase propagation and acceleration of waves. These data sets were obtained using the SWAN (numerical wave model used for the simulation of waves in waters of deep, intermediate and finite depth). This numerical simulation was carried out for the coastal region adjacent to the Patos Lagoon (Veras and Farina, 2013). The thrust force of the vessel engine was represented in exponential form in order to represent the increase (decrease) of the thrust associated with the acceleration (deceleration) of the vessel (Equation (23) and Equation (24)): k = hf x + h 2, y + k (27) 2 k = hfx + h, y + k (28) y = y + k + 2k + 2k + k 6 (29) x = x + h (30) In this way, the trajectory of the vessel obtained by the Runge-Kutta algorithm is estimated using numerical simulations carried out during 30 hrs with the integration time step of 0.1 s. The ship used in the study has and elliptic geometry form with 290 m of length, 37 m of width and ton of mass. The physical parameters used on the simulations are presented on the Table 1. Table 1 Physical parameters used on the numerical simulations Physical parameter Ship length Ship width Ship mass Simulation time Integration pass Initial velocity of the ship Value 290 m 37 m ton 30 hrs 0.1 s 9,7 ms -1 (18.9 knots) E C = e t (103 ) (23) E D = e t (103 ) (24) Where: E c and E d represent the increasing and decreasing thrust of the vessel in Newton (N) as function of time (t). 2.3 Numerical approximations The system of ordinary differential equations represented by the Equation (15) was solved using the fourth order Runge- Kutta method. In this system, the variation (j = 1, 2, 3) represents the number of differential equations used to represent (x, y and θ) degrees of freedom varying over the time x n. h represents the integration step applied during a number of iterations counted by n. k = hfx, y (25) 3 Boundary conditions The wave energy could affect the ship hydrodynamics in different ways (Pontes, 1998). In this study it is emphasized how the numerical simulation in time domain is important to evaluate hydrodynamic behavior of floating structure, and how the waves effect is relevant in simulations. The influence of wind waves on the ship hydrodynamic is investigated using a time series of significant wave height, velocity and acceleration over 30 hrs (Figure 2). During the study period the significant wave height presents a stable pattern in the first hour. The free surface increases after 2 hrs, reaching the maximum value of 0.9 m around 20 hrs of simulation. The velocity (acceleration) presented a Vol. 9 No. 2 pp December 2014 Marine Systems & Ocean Technology 99

30 Preliminary study about the wave influence on the ship hydrodynamics Amanda Armudi, Wiliam C. Marques, Jorge F. C dos Santos, Lucas S. Bravo, Elisa H. Fernandes and Pedro V. Guimarães similar behavior with higher variability occurring after 2 hrs and reaching maximum values of 15.6 ms -1 (7 ms -2 ), around 4 hrs of simulation. The time series of the thrust generated by the engine is presented on Figure 3. Both of the time seriess present high variation during the first seconds of simulation. The increase (reduction) of the thrust occurs in the first seconds of simulation reaching the values of 9.7 x 10 7 N (2.8 x 10 6 N) after 1 hrs (10 0 hrs) of simulation. Thus, by the last 29 hours of simulation, the thrust reaches stable conditions, where the maximum value increases 10x10 7 N, and the minimum value reaches 10x10 4 N. 4 demonstrates the three part of Morisons equation. The first parcel represents the relative drag forces between the fluid and the structure, the second parcel is relative to the acceleration or deceleration of the ship and it has origin in the pressure gradients which arisess on the body ship surface. The third component represents the relative inertial force corrected by additional mass relative to the wave intensity. During the first seconds of simulation (Figure 4C) the thrust is increasing and a small variation associated with the inertia is observed. On the other hand, for the simulation using the decreasing thrust (Figure 4D), less variation is observed for the forcing components during the first seconds ( hours) of simulation. Fig. 2: Time series of wind wave parameters over 30 hours Significant wave height (m), (B) velocity (filled acceleration (dashed line) (ms -2 ). of simulation. (A) line) (ms -1 ) and The small variation during the first seconds (for the increasing thrust condition) can be associated with the inertial effects because the initial thrust value around 10 6 N (Figure 3) is not sufficient to maintainn the initial velocity of the ship. Just in case of the simulation with thrust reduction, the initial variation of the velocity is less intense, therefore, the inertia associated to the movement is less important during the first seconds of simulation. The inertial effects associated with the initial conditions become less important up to 1 hr of simulation and the forces reach a stability level. After 1 hr of simulation, the increasing of the wave effects (Figure 2) contributes for the intensification of the external forces that can be associated with the pressure gradients, which arises on the body ship surface with the increasing of the significant wave height, velocity and acceleration. On the case of the increasing thrust the velocity of the ship reaches the higher level. Therefore, the contributions of the relative effects (associated with the wave and ship velocities) for the drag effects (Figure 4A) and inertia associated with the pressure gradients (Figure 4E) are observed. For the case of decreasing thrust, these effects are most intense (Figure 4B and 4F) however the final contribution for the ship hydrodynamics is few important because of the summed effects. Fig. 3 Times series of the increased (A) and reduced (B) thrust engine over 30 hours of simulation. 4 Results and discussion generated by the The simulations were carried out during 30 hrs and the initial condition for the ship velocity was set by 9.7ms -1. The external forces acting on the ship are related to the influence of the thrust, water density and the wind waves effects at the two directions (x and y) represented by Figure 4. The Figure The vessel velocity is presented in the Figure 5 and before the first hour of simulation the curves present a quite different pattern. The velocity is function of the thrust and for the both simulations some variations are observed for the two components (x and y ) during the first hour of simulation. For the situation with the increased thrust (Figure 5A) the external force of the engine does not maintain the initial velocity of the ship. In this way, the initial velocity is reduced during the first seconds and, with the increase of the thrust after 10-2 hrs, the velocity increases again. On the other hand, for the decreased thrust situation (Figure 5B) the initial velocity is maintained and, with the decrease of the thrust after 10-2 hrs, the velocity decreases up to 10-1 hrs of simulation. During this period of simulation, the thrust is constant and this condition favors the more effective action of inertial forces associated with the initial variation of the ship velocity (Figure 4C and 4D). 100 Marine Systems & Ocean Technology Vol. 9 No.. 2 pp December 2014

31 Preliminary study about the wave influence on the ship hydrodynamics Amanda Armudi, Wiliam C. Marques, Jorge F. C dos Santos, Lucas S. Bravo, Elisa H. Fernandes and Pedro V. Guimarães deviations of the vessel. After 1 hr up to the end of the simulation (Figure 6A), small deflections are observed because of the stabilization of the ship velocity over the external forces induced by the wave effects (Figure 4A and 4B). Fig. 4 External forces calculated by the Morison s Equation for the conditions with increased (A, C and E) and reduced thrust (B, D and F). The filled and dashed lines, represent the forces along the x and y directions, respectively. With the thrust increasing (Figure 3A) and the composition of the relative velocity (acceleration) imposed by the wave effects (Figure 2B), the speed growth reaching 11 m/s, the maximum value of the vessel velocity in this simulation (Figure 5A). For the situation with the trust reduction (Figure 3B), the velocity of the ship decays after 1 hr of simulation (Figure 4B). However, after 2 hrs of simulation, the velocity increases because of the relative velocity (acceleration) imposed by the wave effects (Figure 2B) associated with the contribution of the constant thrust (Figure 3B). At the same period (before 2hrs of simulation), the influence of the external forces (Figure 4) associated with the wave effects are observed and the effects of pressure gradients and drag forces become important causing increasing (reducing) of the ship velocity according with the increasing (reduction) of the wave velocity. On the situation with the thrust decreasing, the variations on the x and y components up to 10-2 hrs of simulation (Figure 6B) are not observed. During this period of simulation, the thrust is constant (Figure 3B) and the initial velocity is maintained, favoring the lower influence of the inertial forces (Figure 4D). With the decrease of the thrust (after 10-2 hrs), the velocity decreases up to 10-1 hrs of simulation (Figure 5B). This condition favors the action of drag and inertial forces, however, in this case are not observed lateral deflections on the ship direction. Between 1 and 2 hrs of simulation, the reduced velocity of the ship (Figure 5B) reflects a lower variation on the ship position (Figure 6B). After 2 hrs up to the end of the simulation (Figure 6B), the stabilization of the ship velocity over the external forces induced by the wave effects contributes for the similar pattern observed on the situation of the increasing thrust. Figure 7 presents the displacement of the vessel after 30 hours of simulation for the situation with increasing and decreasing thrust, respectively. For the situation with increasing thrust (Figure 7A), the different variations on the x and y components up to 10-2 hrs of simulation reflect on lateral deviations of the ship trajectory (Figure 7A). On the other hand, for the situation with decreasing thrust (Figure 7B), the small variations on the x and y components during the whole simulation do not reflect on deflections of the ship trajectory. The position of the ship over the 30 hrs of simulation is presented in Figure 6 for the situation with the thrust increasing and decreasing, respectively. For the situation with the thrust increasing, the ship suffers different variations on the x and y components up to 10-2 hrs of simulation (Figure 6A). Fig. 6 Time series of the ship position (m) for the situation with increase (A) and reduction (B) of the thrust. Filled and dashed lines represent the x and y components, respectively. Fig. 5 Time series of velocity (ms-1) for the situation with increase (A) and reduction (B) of the thrust. Filled and dashed lines represent the x and y components, respectively. During this period of simulation the thrust is constant (Figure 3A) and the external force of the engine does not maintain the initial velocity of the ship (Figure 5A). In this way, the reduction of the initial velocity during the first seconds favors the more effective action of the inertial forces (Figure 4C) contributing for the lateral Fig. 7 Ship displacement for the situation with increase (A) and reduction (B) of the thrust. Vol. 9 No. 2 pp December 2014 Marine Systems & Ocean Technology 101

32 Preliminary study about the wave influence on the ship hydrodynamics Amanda Armudi, Wiliam C. Marques, Jorge F. C dos Santos, Lucas S. Bravo, Elisa H. Fernandes and Pedro V. Guimarães Over 30 hrs of simulation the ship developed a mean velocity of 8.3ms -1 (5 ms -1 ) for the case with the increased (decreased) thrust. In this way, the ship displaced m to the decreased thrust condition, and m in case of the increasing thrust (Table 2). Table 2 Mean velocity and total displacement over 30 hrs simulation. Physical parameters Mean velocity (ms -1 ) Total displacement (m) Increased thrust 8.3 ms -1 (16.2 knots) Decreased thrust 5 ms -1 (9.7 knots) m m 5. Summary and conclusion This work brings a preliminary study about the ideal conditions of navigability for the ships near the coastal and estuarine regions. The simulations were carried out during 30 hrs and the external forces acting on the ship were related to the influence of the thrust, water density and the wind wave effects. Results were investigated under two different conditions with increased and reduced of thrust. The vessel velocity is a function of the thrust and for the both simulations some variations are observed for the two components during the first hour of simulation. For the situation with the increased thrust the external force of the engine does not maintain the initial velocity of the ship. On the other hand, for the decreased thrust situation the initial velocity is maintained and the velocity decreases up to 10-1 hrs of simulation. During this period of simulation, the thrust is constant and this condition favors the more effective action of inertial forces. With the thrust increasing and the contribution of the relative velocity (acceleration) imposed by the wave effects the speed growth. On the other hand, for the situation with the trust reduction, the velocity of the ship increases after 2 hrs of simulation because of the relative velocity (acceleration) imposed by the wave effects associated with the contribution of the constant thrust. At the same period, the influence of the external forces associated with the wave and drag effects are observed. Therefore, the effects of pressure gradients become important causing increasing (reducing) of the ship velocity according with the increasing (reduction) of the wave velocity. The reduction of the initial velocity during the first seconds favors the more effective action of the inertial forces contributing for the lateral deviations of the vessel. After 1 hr up of the simulation, small deflections are observed because of the stabilization of the ship velocity over the external forces induced by the wave effects. On the situation with the thrust decreasing, the variations on the x and y components are not observed. This condition favors the action of drag and inertial forces associated with the wave effects, but in this case are not observed lateral deflections on the ship direction. For the situation with the increasing thrust the variations on the x and y components reflect on lateral deviations of the ship trajectory. Over 30 hrs of simulation the ship developed a mean velocity of 8.3ms -1 (5 ms -1 ) for the case with the increased (decreased) thrust. Therefore, the ship displaced m ( m) to the decreased (increased) thrust condition. The next steps forward on development of this study are considering three-dimensional dynamics of ship, using 6 degrees of freedom and different forms for the ship. After carrying some tests of sensitivity and possible calibration/validation, this numerical model should be coupled to the numerical modeling system TELEMAC, developed by the Laboratoire National d Hydraulic et Environment (Paris, France). The evolution of this work will provide a numerical tool capable to simulate real situations in order to investigate the ideal conditions of navigability for ships entering through the Patos Lagoon estuary. Aknowledgments The authors are grateful to the Agência Nacional do Petróleo - ANP and Petrobras for the fellowships regarding the Programa de Recursos Humanos (PRH-27) that provided bursaries, the Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul (FAPERGS) for sponsoring this research under contract: and to the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) under contracts: / and / Further acknowledgments go to the Brazilian Navy for providing detailed bathymetric data for the coastal area; the Brazilian National Water Agency and NOAA for supplying the fluvial discharge and wind data sets, respectively; and to the open TELEMAC-MASCARET ( for providing the academic license of the TELEMAC system to accomplish this research. Although some data were taken from governmental databases, this paper is not necessarily representative of the views of the government. References AYAZ Z., Vassalos D. and Spyrou K. J. Manoeuvring behavior of ships in extreme astern seas. Ocean Engineering, 33(17-18), BERTRAM V. (1990) - A Panel Method for Ship Motions. Institut fur Schiffbau, Hamburg. 102 Marine Systems & Ocean Technology Vol. 9 No. 2 pp December 2014

33 Preliminary study about the wave influence on the ship hydrodynamics Amanda Armudi, Wiliam C. Marques, Jorge F. C dos Santos, Lucas S. Bravo, Elisa H. Fernandes and Pedro V. Guimarães CHESTER R. (2002) - Marine Geochemistry. Department of Earth Sciences, University of Liverpool. JENSEN, J.J. and Pedersen, P.T. (1979) - Wave-Induced Bending Moments in Ships - a Quadratic Theory. Transactions Royal Institute of Naval Archtects, Vol. 121, pp LIN, R. Q., & Kuang, W. (2010). Numerical modeling of nonlinear ship-wave interactions. Google Patents. Retrieved from PONTES L. G. S. (1998) - The behavior of FSO s under Waves, Currents and Wind. COPPE / UFRJ. MARQUES R. O. (2010) - Análise acoplada dos movimentos de um FPSO e da dinâmica dos sistemas de ancoragem e risers, Master s Dissertation, Universidade Federal do Rio de Janeiro, COPPE. MARUO, H. (1962) - Calculation of the Wave Resistance of Ships, the Draught of Which is as Small as the Beam. Journal Zosen Kiokai, The Society of Naval Architects of Japan,Vol. 112, pp MICHELL, J. H. (1898) - The wave resistance of a ship. Phil. Magazine, Vol. 45, pp SEO M. -G & Kim Y. (2011) Numerical analysis on ship maneuvering coupled with ship motion in waves. Ocean Engineering, 38(17-18), VERAS P. and Farina L. (2013) - The surf zone dynamic of waves in Northern Spain and in Southern Brazil. Basque Center for Applied Mathematics, Bilbao Spain, and UFRGS, Porto Alegre, Rio Grande do Sul, Brazil. YANG, J. (2004) Time domain, nonlinear theories on ship motions. Department of ocean and resources engineering, University of Hawaii. Vol. 9 No. 2 pp December 2014 Marine Systems & Ocean Technology 103

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35 Application of telemac - ecos modeling system at the southern brazilian shelf: case study of Tramandaí beach oil spill Caio Eadi Stringari 1*, Wiliam Correa Marques 2, Leonardo Fagundes de Mello 3 and Renata T. Eidt 1 1 Instituto de Oceanografia, Universidade Federal do Rio Grande, Rio Grande, Brazil. 2 Instituto de Matemática Estatística e Física, Universidade Federal do Rio Grande, Rio Grande, Brazil. 3 Centro de Ciências Computacionais, Universidade Federal do Rio Grande, Rio Grande, Brazil. Abstract This work presents the results of simulation of an oil spill occurred in 26 th January 2012 on Tramandaí beach. The simulations were carried out through the coupling between two numerical models: the hydrodynamic three-dimensional model Telemac3d and the ECOS (Easy Coupling Oil System) which is being developed at Universidade Federal do Rio Grande (FURG). The hydrodynamic pattern, the drift of oil slick, the oil weathering and a risk map are presented. Hydrodynamic results show a wind driven pattern due the action of the winds. The oil drift indicates the spilled oil reaches the coastline after 10 hours. The oil weathering indicates an evaporation of 18% and an emulsification of 70%. Therefore, these effects increase the oil density in 4.6% intensifying its vertical dispersion. Keywords Oil spill modelling, hydrodynamic modelling, Tramandaí beach 1 Introduction As fossil fuel based society, oil spills have been inherent to the oceans. There are daily reports of spills due to harbour, platforms (FSPOs) and ship operations. In addition, oil compositions consist of several long chain and/or polycyclic aromatic hydrocarbonates that once in contact with the environment become toxic compounds, causing a series of processes ranging different timescales and causing chronic and irreversible effects according (Burns et. al 1994). The Southern Brazilian Shelf (SBS) is an environment with specific characteristics. It is characterized by a large continental shelf, located between 28 S and 35 S and is influenced by the presence of two western boundary currents, the Brazil and Malvinas currents, respectively. In fact, the region marks the transition between tropical, subtropical and sub-polar waters with the presence of several different water masses. The influence of the two major freshwater sources, the Patos Lagoon and the La Plata River, is also important for the region dynamics due to the buoyancy driven circulation caused by their freshwater plumes. Finally, near-shore there are the influence of modulated tides, winds and waves interacting with manmade structures and the biggest Southern Brazilian harbour, the Rio Grande harbour complex. This area is ideal for application of numerical models since a number of processes can be evaluated providing good contributions to the knowledge of the dynamics of the region. Moreover, due to the harbour activity, the region is prone to have accidents with oil and other chemical spills. Oil spills in marine ecosystems could generate a series of effects in different temporal and spatial scales and some of them could be irreversible. Numerical modelling of these processes is a powerful tool with low computational cost to investigate the path and behaviour of spilled oil The Southern Brazilian Littoral (Figure 1A and Figure 1B) is a continuous sand line with Southwest-Northwest (SW-NW) orientation, which could be geographically divided in tree major sections: (1) the South Littoral, (2) the Middle Littoral and (3) the North Littoral [2]. Tramandaí beach is located at the North Littoral portion, where the major biodiversity of whole littoral is found due to the more complex local geomorphologic factors (Weschenfleder e Zouain, 2002). Vol. 9 No. 2 pp December 2014 Marine Systems & Ocean Technology 105

36 Application of telemac - ecos modeling system at the southern brazilian shelf: case study of Tramandaí beach oil spill Caio Eadi Stringari, Wiliam Correa Marques, Leonardo Fagundes de Mello and Renata T. Eidt The North Littoral has susceptibility to oil spills due to the presence of oil capture buoys. These buoys are located in the coastal area capturing the oil from tanker ships and transmitting to the Osório oil plant. There are two buoys in this region; however, this work is focused on the nearest buoy from the coastline, located at S W. This buoy is located at the 25 m isobath and is connected with the Osório plant by a 6 km oil-duct and further to the Alberto Pasqualini refinery (REFAP), in Porto Alegre, by a 90 km long oilbuoy with the duct. Figure 1C shows the location of the "+" signal. In accordance with the Brazilian legislation, numerical simulations regarding oil spills may be used to define the area which could be influenced by the activities involving oil. These studies are used to support the environmental diagnostic, such as: the elaboration of risk maps, oil sensitivity charts and contingency plans used by oil companies and environmental agencies (Mello et al, 2012). 2 Methodology 2.1 Hydrodynamic model The hydrodynamic simulation of process was carried out using the three-dimensional finite-elemenmodel Telemac3D ( This model open-source solves the Navier-Stokes equations considering the local variation of the free surface, ignoring the density variation on the mass conservation equation and considering the Boussinesq approximation to solve the momentum equations (Hervouet, 2007). The finite element techniques is used to spatially discretize the hydrodynamic equations considering the sigma levels for the vertical discretization and the Multidimensional Upwind Residual Distribution (MURD) for the advection of three- dimensional variables. A time step of 90s and the Coriolis coefficient of s -1 (latitude 30 S) were used in the hydrodynamic simulation. Following the methodology of Marques et. at, 2012 the horizontal turbulence process was modelled using an adapted Smagorinsky and a mixing length model for coastal areas in order to estimate the horizontal and vertical turbulent processes, respectively. The vertical discretization consists of fifteen sigma levels distributed in such way that the top and the bottom most layers of the water column have more sigma levels than the middle of water column. This type of distribution allows to better represent the superficial and bottom layers which is ideal for oil spills since the processess involved in oil spills are very often restricted either to the first centimetres of the water or, in case of sedimentation, to the bottom. Fig. 1 Study Region. B) Numerical domain and discretization. Detail of the inner shelf with the positions of two transects. D) Detail of the Tramandaí region with location of the oil capture buoy. In this way, the oil spill numerical modelling is a comprehensive tool that might provide support to the environmental agencies and companies. Nevertheless, a powerful hydrodynamic model must be used to represent the ocean conditions near-shore; otherwise, the oil spill model cannot work. Therefore, the objective of this work is to present the application of Telemac3d for providing the ocean state variables to an oil spill model in such a way that is possible to have the high resolution conditions needed to evaluate the oil spill event that occurred in 26th January 2012 within the Tramandaí Coast Oil spill model The behaviour and fate of the spilled oil were investigated using the ECOS (Easy Coupling Oil System) model, registered at the Instituto Nacional da Propriedade Industrial - INPI under contract: BR ECOS is a lagrangian and weathering oil spill model developedd at the Universidade Federal do Rio Grande FURG. This model s major feature is the easiness of the process of coupling it with hydrodynamic models already written. Based and developed within the state change paradigm and written in object-oriented FORTAN 95 language, the ECOS model is subdivided into several modules. Each module is responsible for computing an oil property and some modules have a linkage function. The ECOS model characterizes the main features acting in an oil spill, isolating the processes according to their influence and intra-cooperation. There are several modules and subroutines responsible to evaluate the phenomena in which the oil is exposed. In order to have a better organization and an optimum usage of the structures, the object-oriented programming technique has been used to follow the interrelationships between the physical properties of the spilled oil. 106 Marine Systems & Ocean Technology Vol. 9 No.. 2 pp December 2014

37 Application of telemac - ecos modeling system at the southern brazilian shelf: case study of Tramandaí beach oil spill Caio Eadi Stringari, Wiliam Correa Marques, Leonardo Fagundes de Mello and Renata T. Eidt ECOS handles the oil like discrete particles using lagrangian approximation to evaluate the tracer (particles) proprieties during time. The tracer trajectories are evaluated considering the oil as a large number of particles which move independently in water. The tracer velocities are interpolated at each node of the hydrodynamic numerical domain (Figure 1B). The final tracer position depends on four different factors: (1) current velocity, (2) wind velocity, (4) spreading effect and (4) turbulent diffusion. 3 Numerical domain, boundary and initial conditions The numerical domain (presented at Figure 1B, 1C and 3) consists of a triangular mesh produced with the pre-processor MATISSE. There are nodes and elements within the three-dimensional mesh implying a resolution of 100 meters on the coastal region of Tramandaí and around 0.25 degree at the coarser portions of the mesh at the open ocean. Fig 2. ECOS-Telemac3d Coupling In order to evaluate the hydrodynamics of the SBS, the oceanographic parameters from HYCOM (HYbrid Coordinate Ocean Model, were used in this work as boundary conditions. These data sets present moderate temporal and spatial resolution and also have been used worldwide. Fig. 3 shows the boundary conditions implemented in Telemac3D in which the red line indicates temperature and salinity values, the yellow line indicates the oceanic currents which are prescribed at Northern and Southern boundaries, the blue line indicates tides and low frequency ocean levels which are prescribed only at the Eastern boundary and finally the arrows indicate the air temperature and winds which are prescribed for the whole numerical domain. The module called Environment has the function to gather the environmental variables. The hydrological parameters used by this module are the velocity fields, water temperature, water salinity, water levels, water density and winds. This is the most important module of ECOS since it acts like a data source for the whole rest of the model. It is also the starting point for coupling with hydrodynamic models. Oil weathering is evaluated in a module called Weathering, which receives the information from the Environment module after parameterization. Here the phenomena of evaporation and emulsification are evaluated and the oil density is estimated. The oil slick transport is evaluated by the module called Lagrangian which receives information of the velocity fields from the Environment module and evaluates the phenomena of spreading and turbulent diffusion. The three major river discharges of this region were considered as liquid boundary conditions of the Patos Lagoon through the usage of climatologic data provided by the Brazilian National Water Agency (ANA, ov.br). Ocean currents, low frequency water levels, temperature and salinity with a temporal resolution of 24 hours and a spatial resolution of 0.25 degree were interpolated to each boundary node of the numerical domain. The five major components of the astronomical tides (K1, M2, N2, O1 and S2) were extracted from the Grenoble Model (FES95.2, Finite Element Solution v.95.2) and also interpolated to the boundary nodes of the numerical domain. The outer boundary was forced with winds and air temperature from NOAA reanalysis ( with a temporal resolution of 6 hours and spatial resolution of 0.5 degree. These data were interpolated through the whole numerical domain Coupling between Telemac3d and ECOS The ECOS code was directly coupled to the Telemac3d source code. Hydrodynamics and the wind information from Telemac3d are transferred to ECOS Lagrangian module for the evaluation of the tracer positions at each time step. After all the properties have been evaluated, the final position of each tracer is integrated in time using a second order Runge-Kutta method. Salinity, temperature, and the water density are transferred to ECOS weathering module, which evaluates the oil evaporation, emulsification and density. Figure 2 shows the coupling between these models. For more details regarding the coupling procedure see Mello et. al, Fig 2. Telemac3D boundary conditions. Vol. 9 No. 2 pp December 2014 Marine Systems & Ocean Technology 107

38 Application of telemac - ecos modeling system at the southern brazilian shelf: case study of Tramandaí beach oil spill Caio Eadi Stringari, Wiliam Correa Marques, Leonardo Fagundes de Mello and Renata T. Eidt Telemac3D was initialized with temperature, salinity and velocity varying spatially. A "hot-start" procedure was used: A simulation was carried out between 1 st and 31 st December of 2011, then the last time-step of this simulation was considered as the initial condition for the simulation used in this work, starting at 1 st January of ECOS uses Fay, 1969 formulation to simulate the initial condition for an accidental punctual spill with circular shape. This formulation takes in account the differences between oil and water density and the oil volume to estimate the initial area of the slick based on the different superficial tensions and diffusion coefficients. The initial oil density was 912 kg/m³; the standard water density was 1025 kg/m³ and the spilled oil volume was m³. The information regarding the spill was cordially given by the Brazilian Environmental protection Agencies and the Brazilian Navy. In addition, Telemac3d was calibrated and validated for the investigation of the hydrodynamic, morphodynamic and wave processes along the SBS in previous studies (Marques et al, 2012; Marques et al 2010, Marques et al 2009). Figure 4 shows time series of SSH, winds and surface currents. These time series were obtained at the buoy region shown in Figure 1C and indicated by the + marker. The SSH is in the expected theoretical range for this region with values around 1.0 m. Throughout the simulation a bidirectional behaviour of coastal currents is observed. This pattern relies on the interchange of wind direction due to the passage of frontal meteorological system in this region. This pattern of the wind circulation was identified before for the SBS [5, 6, and 13] and the bidirectional behaviour of the coastal currents was presented at Tramandaí coast by [14, 15]. Figure 5 to 10 show the variability of the coastal currents and SSH in intervals of ten days. Colour gradients and vectors indicate the intensity and direction of the currents whereas white contours indicate values for SSH. 4 Results and discussion 4.1 Hydrodynamic Because the major influences on the oil path in this region are caused by the winds and currents (Stringari et al, 2013), the hydrodynamic results of this work are focused on the behaviour of the costal wind-driven currents and the sea surface height (SSH). Fig 5. Spatial variably of surface currents and SSH for 1st of January Fig 4. Temporal variability of: A) Sea surface height; B) Wind speed and direction; C) Surface currents speed and direction. Fig 3. Spatial variably of surface currents and SSH for 10th of January. 108 Marine Systems & Ocean Technology Vol. 9 No. 2 pp December 2014

39 Application of telemac - ecos modeling system at the southern brazilian shelf: case study of Tramandaí beach oil spill Caio Eadi Stringari, Wiliam Correa Marques, Leonardo Fagundes de Mello and Renata T. Eidt available for the region for a comparison; however, the values found for the currents intensity and direction are compatible with the literature (Costa e Moller, 2011; Jung, 2010) and also the major qualitative features of the austral summer conditions are well represented for the model. In addition, Telemac3d was calibrated and validated for the investigation of the hydrodynamic, morphodynamic and wave processes along the SBS in previous studies (Marques et al, 2012; Marques et al 2010, Marques et al 2009). Two transects were extracted to investigate the vertical circulation pattern. Both transects present the averaged circulation pattern obtained using the vertical and the longitudinal components of the velocity at the given transect. Fig 7. Spatial variably of surface currents and SSH for 20th of January. Figure 9a shows the alongshore transect. This figure presents the north-south oriented circulation similar to the depth-averaged field. A typical shelf circulation is observed with the velocity decreasing in the vertical due to the bottom stress. Moreover, a bottom induced vertical circulation where the bottom topography gradient is more abrupt is also shown. This circulation pattern is typical for extensive shelves with few topographic influences and intense wind dominance as show in the works of Palma et al. 2004, 2008 and Piola et al., 2001 for the Southern Atlantic shelf. (a) Fig 4. Spatial variably of surface currents and SSH for 30th of January. While whether looking at Figure 5 and 6 it is possible to see a change in current directions, all other Figures (6-8) show a pattern with orientation Northeast-Southwest. Where the variations of SSH are more abrupt and the values are lower, the intensity of currents are higher due to the mass conservation and the barotropic transport. Having a look at Figure 6 it is possible to see meanders, probably caused by the bottom influence. Moreover, the southern portion of the region has strong currents which is probably also related to the bottom topography. The influence of the bottom topography modulating the coastal circulation is discussed for the region by Meunier et al, Unfortunately, there was no hydrodynamic data Fig 9. (b) a) Alongshore time-averaged vertical circulation in m.s 1 b) Cross-shore time-averaged circulation in m.s 1. Figure 9b shows the cross-shore transect where an upwelling circulation cell is observed. In this case, the upwelling Vol. 9 No. 2 pp December 2014 Marine Systems & Ocean Technology 109

40 Application of telemac - ecos modeling system at the southern brazilian shelf: case study of Tramandaí beach oil spill Caio Eadi Stringari, Wiliam Correa Marques, Leonardo Fagundes de Mello and Renata T. Eidt favorable winds (north quadrant winds) induce superficial offshore transport and the further replacement of water coming from the external shelf to maintain the dynamic equilibrium of the near-shore region. Similar to the alongstress and the shore transect, the influence of the bottom bottom topography inducing lower velocities near the bottom and major variations of velocity near the abrupt topographic gradients, respectively, is also present. Upwelling circulation cells were noticed on the Brazilian shelf before the South Brazil Bight region (Cape Frio, Cape São Tomé and Cape Santa Marta Grande) by several studies. A concise explanation of the phenomena can be found in Palma and Matano, In that study, the Princeton Ocean Model (POM) was used to evaluate the long-term dynamics of the region. The main conclusions of the work were that despite previous observations (Calado et al, 2010, Castelão and Barth, 2006), the upwelling cell is a persistent feature of the region and the main cause was upwelling favorable winds associated with shelf break bottom-inducedd geostrophic circulation. The Southernmost well-formed upwelling cell was noticed and explained by Campos et al.., 2013 in the region of Cape Santa Marta Grande (27 30º S). The cell observed in this work is similar to the previous ones with the only difference that it is not on a "cape" region. However, the formation causes are the same. 4.2 Oil drift and weathering ECOS was started for the 26 th of January at 12:00 (Brazilian time) and computed tracer positions and oil weathering over the entire spill event. Figure 10 shows the evolution of oil drift for intervals of 1 hour (grey scale). The oil spill follows the direction of mean surface currents and winds, reaching the shore after 10 hours. The extension of the coastal region affected is dislocated circa 5 km more to the south than reported by the Brazilian environmental authorities, even though the final position of the tracers are dislocated the dimensions of the spill are very much similar to the reported. The oil field clearly follows the resulting direction between the wind field and the current field accordi ing to the influence of momentum transfer coefficient which was set to 35% to winds and 100 % for currents. It is also possible to infer that the tracer velocities reduce near the coastline because of the reduction of the current velocities caused by the increase of the bottom stress. Fig 11. Temporal evolution of oil weathering properties. Red line: emulsification, blue line: increase in density and black line: evaporation. All values are expressed in percentage. The oil weathering is represented by the evaporation, emulsification and density shown in Fig. 11. The emulsification rapidly increases from the initial state to approximately 80% while the evaporation slightly increases to approximately 10 % within 10 hours. The changes of the oil properties affect directly the oil density which increases 4.6% within 10 hours resulting in a final value of kg/m -3. This could lead to a sinking process since this value is closer to the salt water density. Therefore, after 5 hours, a small portion of the oil began to sink due to the increase in density. This results in a three- three-dimensional dimensional circulation pattern. This pattern can be observed in the integrated snapshot shown in Figure 12, with the oil particles sinking to nearly 0.45 meter in the water column. Fig 10. Oil drift evolution. Grey scale shows the oil spill duration in hours while colour scale shows the intensity of the currents. Black vectors currents intensity. Red vectors represent the wind direction and intensity. Fig 12. Alongshore view of integrated snapshots for the oil tracers. 110 Marine Systems & Ocean Technology Vol. 9 No.. 2 pp December 2014

41 Application of telemac - ecos modeling system at the southern brazilian shelf: case study of Tramandaí beach oil spill Caio Eadi Stringari, Wiliam Correa Marques, Leonardo Fagundes de Mello and Renata T. Eidt Finally, an initial development of a risk map was carried out. The map shown in Figure 13 evaluates the risk (probability) of the oil slick reaching the coast line. The method is based on the volume spilled, the number of particles and geographic location of the coastline and the tracers (Wojtaszek, 2003). The result shows that the region with the highest risk is a sand dune field near Cidreira city. the Agência Nacional do Petróleo - ANP ( Programa de Recursos Humanos - PRH-27) for the fellowships provided. The authors are grateful to the Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul (FAPERGS) for sponsoring this research under contract: and to the CNPq under contracts: / and / Further acknowledgements go to the Brazilian Navy and Brazilian environmental agency (IBAMA) for the information regarding the oil spill, to the Brazilian National Water Agency (ANA) for the water discharge data, the National Oceanic & Atmospheric Administration (NOAA) for the atmospheric data sets, to the HYCOM consortium for the oceanic data sets and finally to Telemac-Mascaret consortium for providing Telemac modelling system to accomplish this research. Fig 5 Risk (or probability) map for the oil spill event reaching the coastline. References BURNS, K. A., Garrity, S., Jorissen, D., Macpherson, J., Stoelting, M., Tierney, J., and Simmons, L. Y. (1994). The galeta oil spill ii.unexpected persistence of oil trapped in mangrove sediments morlaix twenty years after the Amoco-Cadiz oil spill. Estuarine, Coastal and Shelf Research, 38: Final considerations The conclusions of this work are: The hydrodynamic behaviour is regulated by the winds and bottom topography showing a bidirectional pattern throughout the simulation; The major features of the coastal circulation were well represented by Telemac3d, such as the alternation of the current directions due to the wind field, the coastal meanders and the bottom induced topography. The oil slick reaches the coast line after 10 hours induced by the averaged currents and wind field; The oil weathering is responsible to an increase of 4% in oil density leading the vertical circulation processes of the oil spilled; The main endangered area is a sand dune field near Cidreira city. Acknowledgements The authors thank the Conselho Nacional de Desenvolvimento Científico e Tecnológico - CNPQ and to CALADO, L., da Silveira, I., Gangopadhyay, a., and de Castro, B. (2010). Eddy-induced upwelling off Cape São Tomé (22ºS, Brazil). CALLIARI, L. J., Toldo Jr, E. E., and Nicolodi, J. a. L. (2006). Rio grande do sul 437. In Erosão e Progradação do Litoral Brasileiro, pages Ministério do Meio Ambiente - MMA. CAMPOS, P. C., Möller, O. O., Piola, A. R., and Palma, E. D. (2013). Seasonal variability and coastal upwelling near Cape Santa Marta (Brazil). Journal of Geophysical Research: Oceans, 118(3): CASTELÃO, R. M. and Barth, J. a. (2006). Upwelling around Cabo Frio, Brazil: The importance of wind stress curl. Geophysical Research Letters, 33(3):1 4. COSTA, R. L. and Möller, O. O. (2011). Estudo da estrutura e da variabilidade das correntes na área da plataforma interna ao largo de Rio Grande (RS, Brasil), no sudoeste do Atlântico Sul, durante a primavera-verão de Revista de Gestão Costeira Integrada, 11(3): FAY, J. A. (1969). The spread of oil slicks on a calm sea. Oil on the Sea, Plenum Press, pages HERVOUET, J. M. (2007). Free surface flows: Modelling with finite element methods. John Wiley & Sons, England.JUNG, G. B. (2010). Estrutura e Propagação de Correntes Longitudinais na Praia de Tramandaí - RS. Dissertação de mestrado, Universidade Federal do Rio Grande do Sul. Vol. 9 No. 2 pp December 2014 Marine Systems & Ocean Technology 111

42 Application of telemac - ecos modeling system at the southern brazilian shelf: case study of Tramandaí beach oil spill Caio Eadi Stringari, Wiliam Correa Marques, Leonardo Fagundes de Mello and Renata T. Eidt MARQUES, W. C. ; Fernandes, E. H. L. ; Rocha, Luiz A. O. ; Malcherek, Andreas. Energy converting structures in the Southern Brazilian Shelf: Energy conversion and its influence on the hydrodynamic and morphodynamic processes. Journal of Earth Sciences and Geotechnical Engineering, v. 1, p , MARQUES, W. C., Fernandes, E. H. L., and Moller, O. O Straining and advection contributions to the mixing process of the Patos Lagoon coastal plume, Brazil. Journal of Geophysical Research, 115(C6). MARQUES, W. C., Fernandes, E. H. L., Monteiro, I. O., and Möller, O. O Numerical modeling of the Patos Lagoon coastal plume, Brazil. Continental Shelf Research, 29: Marques, W. C., Fernandes, E. H., Möller Jr, O. O., Moraes, B. C., and Malcherek, A Dynamics of the Patos Lagoon coastal plume and its contribution to the deposition pattern of the southern Brazilian inner shelf. Journal of Geophysical Research, 115. MELLO, L. F., Stringari, C. E., Eidt, R. T., and Marques, W. C. (2012). Desenvolvimento de Modelo Lagrangiano de Transporte de Óleo: Estruturação e Acoplamento ao Modelo Hidrodinâmico TELEMAC3D. In Pesquisas Aplicadas em Modelagem Matemática, volume I, pages Unijui, Ijuí, 1 edition. MEUNIER, T., Rossi, V., Morel, Y., and Carton, X. (2010). Influence of bottom topography on an upwelling current: Generation of long trapped filaments. Ocean Modelling, 35(4): PALMA, E. D. and Matano, R. P. (2009). Disentangling the upwelling mechanisms of the South Brazil Bight. Continental Shelf Research, 29(11-12): PALMA, E. D. and Matano, R. P. (2009). Disentangling the upwelling mechanisms of the South Brazil Bight. Continental Shelf Research, 29(11-12): PALMA, E. D., Matano, R. P., and Piola, A. R. (2004). A numerical study of the Southwestern Atlantic Shelf circulation: Barotropic response to tidal and wind forcing. Journal of Geophysical Research, 109(C8):1 17. PALMA, E. D., Matano, R. P., and Piola, A. R. (2008). A numerical study of the Southwestern Atlantic Shelf circulation: Stratified ocean response to local and offshore forcing. Journal of Geophysical Research, 113(C11010):1 22 PIOLA, A. R., Matano, R. P., Palma, E. D., Möller, O. O., and Campos, E. J. (2005). The influence of the Plata River discharge on the western South Atlantic shelf. Geophysical Research Letters, 32(1):1 4. STRINGARI, C. E. (2013). The influence of winds and coastal currents on the oil spill event : Case study of Tramandaí Beach, 26 th January In II Conferência Internacional em Tecnologias Naval e Offshore: Energia e Sustentabilidade - NAVTEC Rio Grande, Brazil TOLDO JR., E. E., Almeida, L. E. S., Dillenburg, S. R., Tabajara, L. L., and Borghetti, C. (1993). Parâmetros Morfodinamicos e Deriva Litoranea da Praia de Tramandaí - RS. GEOSUL, 15(1): WESCHENFLEDER, J. and Zouain, R. N. A. (2002). Variabilidade Morfodinâmica das Praias Oceânicas entre Imbé e Arroio do Sal, RS, Brasil. Pesquisas em Geociências, 29(1):3 13. WOJTASZEK, K. (2003). Application of transport model for building contingency maps of oil spills on the North Sea. Master of Science Thesis. 112 Marine Systems & Ocean Technology Vol. 9 No. 2 pp December 2014

43 Insight into the usage of turbine current converters on the Southern Brazilian Shelf Eduardo de Paula Kirinus 1* ; Wiliam Correa Marques 2 and Helena Barreto Matzenauer 2 1 Instituto de Oceanografia, Universidade Federal do Rio Grande, Rio Grande, Brazil 2 Instituto de Matemática, Estatística e Física - Universidade Federal do Rio Grande - FURG - Rio Grande, Brazil * Corresponding author: ekirinus@gmail.com Abstract The continuous growth of the world population increases the demand and competition for energy, requiring an immense effort for nonrenewable energy sources availability. Application of marine currents for electricity generation could offer a distinct advantage over other renewable energy sources due to the regular and predictable nature of the resource. Therefore, in addition to promoting the development of new technologies, global policies for the generation of renewable and clean energy are being strengthened. Several methods of energy conversion have been developed over the years, especially the turbine-based current energy converter, which demonstrated high energy generation capacity and that have already been in operation. The tridimensional model TELEMAC3D was used to investigate the hydrodynamic processes. This model was coupled with the energy conversion module in order to prospect the best energy spots for marine current energy in the Southern Brazilian Shelf. The study area has shown two viable regions with high potential for exploitation of energy from marine currents, however, the more viable region for the installation of current converters is the northern region, bounded between the Conceição Lighthouse and the Solidão Lighthouse, reaching an average power around 10 kw/day and integrated values of 3.5 MW/Year. The highest levels of power generation were found at intervals of 16 days, showing high correlation with events associated with the passage of meteorological fronts along the study region. This paper details the design of a turbines farm containing ten helicoidal turbines. With three grids a study computing one year of simulation with the TELEMAC-3D model coupled with the energy conversion module was carried out. It was possible to indicate an interest area for trial tests of modelling a turbine farm. The northern region site, on the structural scenario, stands out keeping high conversion rates during events of great potential energy. This improvement happens due to the intensification effects of the current field associated with the presence of the physical structure which enhances the efficiency of the site. No significant differences on the temporal variability pattern between the simulations studied were estimated, showing that the presence of the structures does not impact on changes in the energy conversion temporal pattern on the temporal scales studies in this work. The configuration settled for this study predicted an annual power output of 144,54 GWh which is equivalent to 0,53% of the whole energetic consumption of the Rio Grande do Sul State in Keywords: Coastal Currents; Energy Potential; Conversion Sites; TELEMAC3D; Finite Element Method. 1. Introduction The oceans are an important and infinite source of renewable energy (Cruz and Sarmento, 2007). Such energy can be obtained from waves, tide oscillations or tidal currents, ocean thermal energy (OTEC), the osmotic gradient and ocean currents. Two ways to obtain energy from the currents are through potential energy variations in the sea level) and kinetic energy (ocean currents and their water masses). In general, the technique is defined as undersea wind power. According to Khan et al. (2009), the energy from river and estuary flow, tidal currents and other artificial water channels is considered a viable source of renewable energy. Vol. 9 No. 2 pp December 2014 Marine Systems & Ocean Technology 113

44 Insight into the usage of turbine current converters on the Southern Brazilian Shelf Eduardo de Paula Kirinus; Wiliam Correa Marques and Helena Barreto Matzenauer Several methods of energy conversion have been developed over the years, especially the turbine-based current energy converter, which demonstrated high energy generation capacity and is already in operation. The technique used can be described as an underwater wind turbine, having approximately the same principles of function currents that flow over the shelf break (Piola and Matano, 2001); these factors exhibit large seasonal variations in their physical parameters. TheCanadian Hydrology Center (CHC) conducted a survey of the available marine energy in the Canadian coastal region (Cornett, 2006). This study demonstrated that the average electrical power at 190 study points would constitute approximately 63% of Canadian energy demand. Defne (2010) investigated the energy potential of waves and tidal currents along the south-eastern coast of the United States and identified a power conversion that ranged between 1.0 and 3.0 MW/year. Additionally, EPRI documented 16 TWh/year (4.4 GW/year) in Alaska and 0.6 TWh/year (166 MW/year) in Puget Sound (EPRI, 2006f,e,a,b,c,d). In Brazil, approximately 80% of the population lives within 200 km of the coastline (IBGE, 2010) and also there is no mapping of the coastal zones regarding the energetic potential viable for conversion using hydrokinetic turbines, however, recent studies have showed two spots of high power availability off the shores of the Rio Grande do Sul state, that can generate 3.5 MW/year of power (Kirinus, et. al 2012). Marques, et al (2012) studied the influence of hydrodynamic and morphodynamic processes of the installation of six hydrokinetic turbines reaching 5 GW/year annual power. The SBS, located between 28 os and 35 os (fig. 1 a.), presents a slightly rugged shoreline, which is oriented northeast - southwest. The bathymetry of this region is quite soft, with the higher slope and shelf break located near the 180m isobath. The Patos Lagoon has a drainage basin with approximately km. Its principal tributaries are the Jacuí and Taquari River, which together converge their water fluxes into the Patos Lagoon trough the Guaíba River. Normally during the end of autumn and beginning of the spring seasons, occurs the maximum river flows with an annual average discharge rating around m3/s (Marques et al., 2012). F i g. 1 : A ) S o u t h e r n B r a z i l i a n S h e l f, w i t h m a x i m u m d e p t h a r o u n d m. B ) G r i d u s e d o n t h e s i t e s i m u l a t i o n. T h e r e d s q u a r e r e p r e s e n t s t h e s p o t o f t h e h y d r o k i n e t i c t u r b i n e s f a r m. A l s o, t h e f i n i t e e l e m e n t s m e s h h i g h l i g h t i n g t h e l i q u i d a n d s u r f a c e b o u n d a r i e s c o n d i t i o n s f o r t h e T E L E M A C 3 D m o d e l. Located near the Brazil-Malvinas confluence zone, the study area is known for its high spatial and temporal variability (Podestá, 1997) and the convergence of several water bodies (Möller et al., 2008). Thus, the Southwest Atlantic Ocean is one of the most dynamic regions of the global ocean (Piola and Matano, 2001), characterized by large thermohaline contrasts and intense mesoscale activity (Gordon, 1989). In the SBS region, the confluence of water masses from various origins occurs (e.g., tropical, subantarctic and continental origins). This confluence leads to a dynamic environment with a large thermohaline contrast. SBS circulation is primarily influenced by the plume from the La Plata River, winds and the intensity of the western boundary The high seasonality of the wind fields (Piola et al., 2005) is characterized by the dominance of northeast (NE) winds during the summer and southwest (SW) winds during the winter, which drive the coastal circulation through the SW and NE, respectively (Möller et al., 2008; Marques, 2009; Marques et al., 2010b, 2012). These winds can be enhanced by El Niño Southern Oscillation (ENSO) events (Piola et al., 2005). Recently, the annual energy report of the Rio Grande do Sul state (Capelleto and De Moura, 2010) have briefly mentioned the energy from the marine currents as a possible source for harvesting power, which could easily enhance the Brazilian matrix of energy. Following, the aim 114 Marine Systems & Ocean Technology Vol. 9 No. 2 pp December 2014

45 Insight into the usage of turbine current converters on the Southern Brazilian Shelf Eduardo de Paula Kirinus; Wiliam Correa Marques and Helena Barreto Matzenauer of this paper is to study the potential of using energy converters (as turbine type) along the Southern Brazilian Shelf, applying a three-dimensional model of ocean circulation coupled with an energy model, in order to evaluate the energy conversion and the local circulation pattern of a converters farm. 2 Methodology 2.1 Hydrodynamic model from currents into electrical power were performed with the energy module (Marques, et al. 2012). This module uses the turbine standard equation to calculate the electric power converted in watts (W), from the incident flow velocity. Based on the principle of energy conservation, during each time step of the hydrodynamic model (Fig. 2) the current velocity is calculated and transferred to the energy conversion module that converts some part of the energy of the currents into power through the electric power equation (1). In the energy conversion module the current velocity is updated to maintain the energy balance of the TELEMAC-3D model. The TELEMAC system, developed by the Laboratoire National d Hydraulique et Environnement of the Company Eletricité de France (CEDF), was used for the hydrodynamic simulations. The TELEMAC-3D model solves the Navier Stokes equations by considering local variations in the free surface of the fluid, neglecting density variations in the mass conservation equation, and considering the hydrostatic pressure and Boussinesq approximations to solve the motion equations. The model is based on finite element techniques to solve the hydrodynamic equation (Hervouet, 2007) and relies on the sigma coordinate system for the vertical discretization in order to follow the surface and bottom boundaries (Hervouet and Van Hareen, 1996). A time step of 90s and a Coriolis coefficient of x 10-5 rad.s-1 (latitude 32ºS) were used in all the simulations. The horizontal turbulence process was performed using the Smagorinsky model. This closure turbulent model is generally used in maritime domains with larger-scale eddy phenomena, calculating the mixing coefficient by considering the size of the mesh elements and the velocity field (Smagorinski, 1963). The mixing length model for buoyant jets was implemented to assess vertical turbulence processes. This model takes into account density effects via a damping factor that depends on the Richardson number to calculate the vertical diffusion coefficients. 2.2 Energy conversion module The power of the oceanic currents can be transformed, by using converters with similar technology of wind converters, through a submerged rotor that is forced to rotate by the fluid surrounding it. According to (Khan, et al. 2009), studied equipments available to capture hydrokinetic energy, it was found 76 equipments, among them, turbines in operation or still in the early stages of research were studied. The hydrodynamic simulations used in this work were performed using TELEMAC3D model, and the investigations that involved the energy conversion Fig.2 Fluxogram of the interactions between the TELEMAC3D and the energy module. (Adapted from (Marques, et al. 2012). On According to (Marques, et al. 2010, 2012; Möller, 2008), among others, the region of the SBS presents a multidirectional and highly dynamic pattern of circulation, which are strongly influenced by the passage of frontal meteorological systems. Due to this pattern, in this work the Gorlov converter will be used (Gorlov, 2010) because of its advantages on capturing energy in multidirectional currents. Furthermore, the helicoidal turbine of Gorlov has a sectional area corresponding to a rectangle (h*d) and its efficiency coefficient (η) is smaller, being equal to 0.35 (Gorlov, 2010). Therefore, Equation (1) controls the power gained from a helicoidall converter, where η is the efficiency coefficient of the turbine, ρ is the density of the water, h is the height of the turbine, D is the diameter of the blade and v is the incident velocity intensity. Table I indicates the turbine technical parameters. P(W) = 0.5.ηρ(h*D)v³ (1) Vol. 9 No. 2 pp December 2014 Marine Systems & Ocean Technology 115

46 Insight into the usage of turbine current converters on the Southern Brazilian Shelf Eduardo de Paula Kirinus; Wiliam Correa Marques and Helena Barreto Matzenauer 2.3 Scenario study To investigate the potential for energy conversion and the influence of the installation of energy converters in the natural hydrodynamic processes of the SBS, three simulations were carried out over 365 days, applying the physical parameters established in the upcoming section. The simulated period covers from January 01 st to December 31 st of a climatologic year. One simulation was conducted using only the hydrodynamic processes. After indicating the interesting areas, another mesh was created with ten turbines (Fig. 3.a). The farm grid direction (Fig.3.b) was idealized to be parallel to the coast, with 200 m of distance between each turbine on x and y directions. Due to computational limitations the best shape for a turbine was with 4 nodes (Fig. 3.c), with 10 m distance between each node. The conversion model interacts with the turbine, acquiring the velocity at the node (red bullet at Fig. 3.c), this velocity is converted into power and the loss of kinetic energy is released on the turbine node, represented for the yellow bullets. In order to improve this scenario, the energy sink for conversion was implemented in two simulations with the farm grid (according to the interactions above). One simulation without the conversion structures; and another simulation with the three-dimensional physical structure of the turbines (Fig. 3.d), where the turbine nodes depth were changed on the FORTRAN source code. Table 1 Turbine technical parameters Start-in Speed Cut-in Speed Nominal Power Turbine Height Turbine Ray 0.2 m/s 1.5 m/s 170 kw 14 m 10 m Efficiency coefficient 0.35 Fig. 3 Region of the turbines on the study area. (A) Numerical grid with high degree of refine on the interest region. (B) Converters farm with 10 helicoidal turbines represented with 2 arrays parallel to the coast. (C) Scheme showing the interactions between the energy conversion module and the turbines. (D) Conversion structures represented in a three dimensional shape. The depth of this site is around 18m. 2.4 Initial and boundary conditions In order to study the tendency of power generation and the understanding of the processes occurring within a farm of turbines, for this study we used climatology data to impose the initial and boundary conditions. This data was created from long scale data base from the Brazilian National Water Agency (ANA), the Ocean Circulation and Climate Advanced Modelling Project (OCCAM) and also from Reanalysis (National Oceanic Atmospheric Administration - NOAA). 116 Marine Systems & Ocean Technology Vol. 9 No. 2 pp December 2014

47 Insight into the usage of turbine current converters on the Southern Brazilian Shelf Eduardo de Paula Kirinus; Wiliam Correa Marques and Helena Barreto Matzenauer The climatological changes were performed through a monthly mean of temporal data series of discharge since January of 1940 until December The OCCAM data were treated from 1990 to 2004 for the velocity components, temperature, salinity and sea surface height. The wind and air temperature fields from Reanalysis were gathered from 1948 to 2012 (Kalnay, et al. 1996). The oceanic boundary was forced by the astronomical tides, water levels, current velocity, salinity and temperature fields (Fig. 1.b.). Along the surface boundary, the temporal and spatial variability of the winds and air temperature were prescribed. The air temperature data along the ocean's surface have also been used in order to consider the process of heat exchange with the atmosphere in the model calculations. The numerical model was initialized from the rest and with an initial elevation of 0.50 m, the approximate average tide in the region (Möller, 2008). Along the oceanic border the amplitude and phase data were also prescribed, through the calculation by the Grenoble Model FES95.2 (Finite Element Solution v. 95.6). southern region has less viability for installation of marine turbine currents in the SBS, while the northern region has emerged as a significant potential power producer reaching mean values of 10 kwday -1 and integrated values of 3.5 MW/Year. Therefore, only the northern region is investigated. 3.1 Current pattern and energy conversion In order to define which scenario delivers the most efficiency for a farm of turbines (with or without the presence of the structures), the spatial variability analysis (Fig. 5) was performed considering the temporal variation of the simulation. This analysis relies on the quantification of each turbine on its own capacity of converting the current energy into power according to the hydrodynamic pattern. The rotational pattern was studied in order to understand the tendencies to maintain the turbulence in each scenario. 2.5 Calibration and validation Monteiro et al. (2006) presented results for the calibration and validation of the two-dimensional model in the Patos Lagoon estuary. Subsequently, Marques et al (2009,2010a,b, 2012) performed a set of simulations for the calibration and validation of the threedimensional numerical model along the area covered by the Patos Lagoon and the adjacent coastal region. The results of these calibration and validation tests indicated that the TELEMAC3D model can be used for studies of the SBS with an acceptable degree of accuracy. As a result of these studies, values for many physical parameters (such as the wind influence coefficient, friction coefficient and turbulence models) were available and used to conduct this study. (A) 3 Results The hydrodynamic conditions of this region are characterized by the clash of different water masses. In these regions the average velocity of the current (Fig. 4) was analyzed, and mean values reaching extremes of 0.4 m/s in these two highlighted regions were observed. This mean value is associated with some variability, and thereby the standard deviation of the current velocity is distributed by the same regions of high mean values (Fig 4). This result suggests that: while these regions are appropriate for the location of energy converters, they can also go through periods of low power generation, since the velocity deviation has a closer value to the average. Kirinus, et. al (2012) in previous study, concluded that the Fig. 4 (B) A) Average current velocity (m/s) and its standard deviation (B) during the whole period of simulation. In detail, the southern region in the red-dashed area, and the northern region on the black-dashed area. Vol. 9 No. 2 pp December 2014 Marine Systems & Ocean Technology 117

48 Insight into the usage of turbine current converters on the Southern Brazilian Shelf Eduardo de Paula Kirinus; Wiliam Correa Marques and Helena Barreto Matzenauer The average behaviour of the power generation on both sites was analyzed considering the residual velocity field associated with the mean field power converted (showed in isolines of power in Fig. 5). The average power converted reaches values higher than 1.4 kw (Fig. 5.a and Fig. 5.b) in some turbines. The simulation without the structure presence (Fig. 5.a) shows the higher mean power on the turbines 1, 2, 3 and 6 (counting from the North-West turbine as first and the South-East as tenth, see Fig. 11). Despite this, the simulation with the presence of the structures (Fig. 5.b) shows enhanced power generation at the turbines 7, 8 and 10, in addition those cited before. (A) wake generated by the adjacent turbines. This effect means that the flow incident into a boundary (in this case a turbine) will therefore generate vortices that move downstream at a speed smaller than the upstream incident velocity and it will return to its balance momentum in time (Hardisty, 2009; Kundu and Cohen, 2002). On the simulation without the structure presence (Fig 5. a), this wake effect is purely hydrodynamic, where variations on the velocity fields occurs due to the conversion of the energy which inputs changes on the local vorticity pattern. On the other hand, on the simulation with the structure effect (Fig 5. b), this process shows as a contribution of the alterations into the hydrodynamic processes and the effect of the turbine body shape. These reduction-increasing effects were also observed by Myers and Bahaj (2012) on experimental trials in a flume tank. The superficial vorticity pattern of each scenario is represented in figure 6. The vectors represent the surface residual velocity, while the colours represent the extents of the turbine wake, in both figures it can be observed the same residual pattern, although main differences relies on the turbines wake. On the scenario without the structure presence (Fig. 6 a.) it can be observed more intense curls (both cyclonic and anti-cyclonic) than on the scenario with the presence of the vertical structures (Fig. 6 b.). This result corroborates with the previous residual analysis, showing that the effect of the conversion module alone (Fig. 6 a.) can promote the generation of stronger curls, which led to increase the superficial turbulence. This rotation effect decreases the intensity of the superficial flow, meaning that the turbine behind the wake path will be affected negatively by this strong curl, decreasing its efficiency. Fig. 5 (B) Residual velocities of the entire water column and the mean power (kw) generated for the turbines as isolines. (A) Site without the structures. (B) Site with the presence of the structures. The same South-West circulation pattern can be observed on both simulations, which can be explained by the North quadrant winds dominance during the analyzed period. Besides, there is a slightly intensification at the residual velocity on the simulation that consider the structure effects (Fig. 5.b), with enhanced vectors between the turbine arrays and around them. Behind the turbines we can observe a shadow zone in the circulation pattern, which can be related with the Despite the same pattern can be observed on the scenario with the structures (Fig. 6 b.), the curl is smoothed indicating that the fluxes surrounding the turbines are more homogeneous distributed resulting in less rotation. The superficial current remains well orientated, decreasing the loss of velocity due to eddy and curl effects. In this case, the entire farm of turbines receives a slightly stronger current, resulting in higher conversion rates. The bottom layer curl (Fig. 7), shows the same pattern as observed on the surface layer, while the absence of structures (Fig. 7 a.) creates higher curls which can deplete the velocity dissipating energy, the presence of the vertical structures (Fig. 7 b.) generates weaker curl retaining the current energy that will be therefore used for the energy conversion. Due to these results, for now on, only the scenario with the presence of the vertical structures will be analyzed. 118 Marine Systems & Ocean Technology Vol. 9 No. 2 pp December 2014

49 Insight into the usage of turbine current converters on the Southern Brazilian Shelf Eduardo de Paula Kirinus; Wiliam Correa Marques and Helena Barreto Matzenauer 3.2 Temporal variability analysis (A) (A) Fig.6 (B) Superficial residual velocities and the rotational pattern (A) Site without the structures. (B) Site with the presence of the structures. Arrow scale of 0.1 m/s. Fig.7 (B) Bottom residual velocities and the rotational pattern (A) Site without the structures. (B) Site with the presence of the structures. Arrow scale of 0.05 m/s. In order to analyse the temporality of the energy conversion regarding the entire turbines farm, time series (Fig. 8 a.) of electric power accounting for the ten converters were taken to perform the wavelet method described by Torrence and Compo (1997). The wavelet method is able to demonstrate the occurrence of events of energy conversion regarding time scales through local and global wavelet power spectrum. At the analysis of the local power spectrum (Fig. 8 b.) positive correlations (red-colour contours) are enhanced for the occurrence of velocities higher than 0.5 m/s, increasing the energy conversion. It also shows that the physical processes maintaining the behaviour of the turbines farm are controlled by two main groups of temporal scales. The first group with occurrence around 6 days dominate the period, forced by the cyclic changes of the wind pattern direction. Fig. 8 Integrated current velocity and electric power time series (A) used for the cross-wavelet analysis, as well as, the local (B) and the global (C) wavelet power spectrum of the time series using Morlet wavelet. Thick contour lines enclose regions of greater than 95% confidence for a red-noise process with a lag- 1 coefficient of Cross-hatched regions indicate the cone of influence where edge effects become important. Vol. 9 No. 2 pp December 2014 Marine Systems & Ocean Technology 119

50 Insight into the usage of turbine current converters on the Southern Brazilian Shelf Eduardo de Paula Kirinus; Wiliam Correa Marques and Helena Barreto Matzenauer Otherwise, the second group of temporal scales consists of correlations covering periods above 16 days, suggesting that the physical processes shorter than 20 days were the main mechanisms controlling the electric energy conversion along the inner continental shelf. The global spectrum of energy (Fig. 8 c) corroborate this hypothesis, indicating with 95% of confidence, the occurrence of processes with time scales above 16 days and may be extended in some moments, throughout the study period. This pattern is similar to the obtained by Marques, et al. (2012) with respect to the occurrence of the processes and cycles of occurrence. Thus are strongly influenced by the passage of frontal meteorological systems generating further changes in wind direction and intensity of currents. 3.3 Spatial variability analysis In order to define the importance of each turbine in the farm structure, the correlation between the incident current velocity and the power was performed along the turbine arrays. With this analysis, the efficiency of each turbine was studied in different time scales behalf the usage of bidimensional cross-spectral wavelet analysis, considering that the dominant processes occurring on the turbines site have temporal scale higher than 1 day and lower than 30 days. The importance of each turbine and its variance in time is defined by the high correlation (red colored contours) in the Morlet Wavelet. Values on the right of the tendency line indicate with 95% of confidence the best placed turbines. For the simulation considering the presence of the structures, through the cross-spectral (Fig. 9 a.) it can be observed intensification on the power conversion in several turbines during the main conversion events. The temporal series of mean variance (Fig. 9 b.), indicated with 95% of confidence that the four events of great power conversion sustain high power and are also intensified in this scenario. Variance values above 35 kw (Fig. 9 b.) can be observed during the October extreme event, enhancing the greatest power capacity of this scenario. The mean variance of each turbine (Fig. 9 c.) indicates that the higher correlation between the variables maintain average power around 7 kw. Moreover, it suggests that the turbines 1, 2, 3, 6 and 7 are the most efficient of the farm, considering only the energy conversion. This discrepancy between the turbines efficiency relies on their positions on the farm and the influence of the incident current into the wake patterns. Fig.9 (A) Cross-spectral analysis between power (kw) and current velocity (m/s), for events with scale period higher than 1 day and lower than 30 days. Thick contour lines enclose turbines of greater than 95% confidence for a red-noise process with a lag-1 coefficient of (B) Mean variance of the studied period, where values beneath the tendency line represents 95% of confidence. (C) Temporal series of the spacial mean variance of each turbine. 3.4 Events of high energy conversion The velocity time series (Fig. 8 a.) and the variance time series (Fig. 9 b.) show four events of high energy conversion during the entire year, in order to analyze the pattern of occurrence of these events and its influence on the vertical fluxes surrounding the farm of turbines, two main events were chosen. For that, the May event and the event at the end of September were chosen and it will be referred to, in this section, as event I and II, respectively. In both, time series of winds intensity and direction (Fig. 10) were taken in order to identify the mechanism behind each event. Furthermore, vertical cross sections were analyzed during these periods. The event I is characterized for south winds reaching 10 m/s, while event II have strong north winds with 15 m/s of intensity. Despite the difference in the wind direction, the high intensity winds are the main mechanism of these high energy conversion events. Thus is due to the high dominance of southwest and northeast winds in the region, and moments with high intensity have high correlation with the passage of frontal meteorological systems. As a result, event I can promote 60 kw conversion on the first turbine, while event II almost 120 kw (Fig. 10 c and d, respectively). The residual currents of these events show that the currents are very influenced by the wind direction. According to Marques, et al (2010), wind-setup is the main mechanism to control the meso-scale dynamics on the SBS. As the wind changes direction and increase intensity (Fig. 10 a. and b.), it drives the coastal currents to the same direction, and in this case, promotes high energy conversion to the turbines. Three cross sections (A, B and C) were taken with the direction northeast-southwest with starting point on 0 meters mark (Fig. 11) and ending point at meters. The cross sections represent in vectors the transversal velocity while the colored surface represents the vertical velocity. 120 Marine Systems & Ocean Technology Vol. 9 No. 2 pp December 2014

51 Insight into the usage of turbine current converters on the Southern Brazilian Shelf Eduardo de Paula Kirinus; Wiliam Correa Marques and Helena Barreto Matzenauer (A) Fig. 11 Location of the vertical cross section. The cross section initiates at 0m (above the turbine 1 and 6) and ends in m (below turbines 5 and 10). Cross section A is on the left side of the farm of turbines, while cross section C is on the right side. Cross section B in the middle of the farm. Numbers of each turbines. (B) (C) The fluid motion follows the wind setup in both events (Fig. 10 c. and d.). In event I the cross section analysis (Fig. 12) shows an intensification of the southern turbines can be observed due to their position in relation to the incident current (northeast wind-driven current as showed in Fig. 10. c.). The cross section C (Fig 12 c.) shows the bottom current encountering the conversing structures (400 to 1200m). Previously of this meeting, the currents are intensified due to the wind-setup and then, after the energy conversion, it suffers a velocity loss of 35%, which is same value of the turbine efficiency designed for the study (see table 1). In event II (Fig. 13) we can observe that the wind-setup controls the current, directing the entire water column into the southwest direction (Fig. 10 d.). Despite, in cross section A (Fig. 13 a.), a slightly reduction in the velocity flow at the mid-bottom layer at the south of the farm (1200 to 1800m distance), the flow maintain its direction. Thus is a reflex of the wake pattern generated by the turbine farm that at the end of the wake, results in decreased velocities and dissipation of energy. This effect is smoothed in cross section B and C. In comparison, both events relies their main mechanism to the wind intensity. In addition, due to the farm configuration, there will be always one turbine highly affected by the farm wake. The main direction of the current inhibits the last turbine of the event to reach the maximum efficiency, in event I is the 1 st turbine, while event II is the 5 th turbine. Fig.10 (D) Wind intensity during the events of high energy conversion. (A) Event I with southern winds and (B) Event II with north winds. Residual currents and conversion rates during the events I (C) and II (D). 4 Conclusions The Southern Brazilian Shelf is highly dynamic and constantly influenced by cycling winds (North-East/South- West) and the wind-driven coastal currents. This condition makes the usage of marine current turbines viable, although the recommended helicoidal turbine is to be applied. From this work we can conclude that: The comparison between the simulations with and without the presence of the physical converting structure demonstrated Vol. 9 No. 2 pp December 2014 Marine Systems & Ocean Technology 121

52 Insight into the usage of turbine current converters on the Southern Brazilian Shelf Eduardo de Paula Kirinus; Wiliam Correa Marques and Helena Barreto Matzenauer that, regarding the numerical aspect of these simulations, the effect of the structure does not input changes on the temporal pattern of the energy conversion. The structures presence acted in a positive way in order to promote the intensification of the velocity field surrounding the turbines farm, also increasing the energy conversion. (A) (A) (B) (B) Fig.13 (C) Vertical cross sections during the event II. (C) Fig. 12 Vertical cross sections during the event I. The presence of the energy converters, on the other way, removed some part of the kinetic energy from the coastal currents, generating divergence and convergence zones in accordance with the dominant direction of the currents. The 122 Marine Systems & Ocean Technology Vol. 9 No. 2 pp December 2014

53 Insight into the usage of turbine current converters on the Southern Brazilian Shelf Eduardo de Paula Kirinus; Wiliam Correa Marques and Helena Barreto Matzenauer changes into the hydrostatic balance generated instability on the fluid motion, - part due to the converting energy, and part due to the presence of the structure generating the wake effect behind the turbines. This effect decrease the energy conversion on the subsequent turbine, although, it also creates an intensification on the surrounding velocity fields. Turbulent process decreases the intensity of the superficial flow, meaning that the turbine behind the wake path will be affected negatively by this strong curl, decreasing its efficiency. The structural scenario this effect was smoothed indicating that the fluxes surrounding the turbines are more homogeneous distributed resulting in less rotation, decreasing the dissipation of energy for the curl. The mechanism behind events of high energy conversion is the wind-setup with intensities up to 10 m/s. The energy conversion associated with the turbine farm geometry generates decreased velocities at the north of the farm on the event I, and the opposite in event II. During both events, slightly differences on the vertical flow structure is observed, demonstrating that during a high wind intensity event, despite its direction, the entire water column stay almost steady increasing the energy conversion in all turbines excepts those influenced negatively for the turbine wake effect. The turbines farm shows great capacity for converting the currents energy, principally during the four main energetic events observed. Regarding the annually energy capacity, this turbine farm can reach 144,54 GWh (16,5 MW*8760 hours) with ten turbines, which is equivalent to 0,53% of the whole energetic consumption of the Rio Grande do Sul State in Further studies shall improve the geometry of the farm and also promote trial test to implement a diffuser structure nearby the turbines to intensity the incident current fields. Acknowledgments The authors are grateful to the Agência Nacional do Petróleo - ANP and Petrobras for the fellowships regarding the Programa de Recursos Humanos (PRH-27) that provided bursaries, the Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul (FAPERGS) for sponsoring this research under contract: and to the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) under contracts: / and / Further acknowledgments go to the Brazilian Navy for providing detailed bathymetric data for the coastal area; the Brazilian National Water Agency and NOAA for supplying the fluvial discharge and wind data sets, respectively; and to the open TELEMAC-MASCARET ( for providing the academic license of the TELEMAC system to accomplish this research. Although some data were taken from governmental databases, this paper is not necessarily representative of the views of the government. References BRAGA, M. F. and Krusche, N. (2000) Padrão de ventos em Rio Grande, RS, no período de 1992 a Atlântica, 22: CAPELETTO, G. J. and De Moura, G. H. Z. (2010) Balanço Energético do Rio Grande do Sul 2010: ano base CORNETT, A. (2006) Inventory of Canada s marine renewable energy resources. Technical report, Canadian Hydraulics Center. CHC-TR-041. CRUZ, J. M. B. P. and Sarmento, A. J. N. A. (2007) Sea State Characterization of the Test Site of an Offshore Wave Energy Plant. Ocean Engineering, (24): DEFNE, Z. (2010) Multi-Criteria assessment of wave and tidal power along the Atlantic coast of the southeastern USA. PhD thesis, Georgia Institute of Technology. DOUGLAS, C. A., Harrison, G. P., and Chick, J. P. (2008) Life cycle assessment of the Seagen marine current turbine. In Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment, page 1:12. v EPRI (2006a) - Maine Tidal InStream Energy Conversion (TISEC): Survey and Characterization of Potential Project Sites. EPRI-TP-003-ME. EPRI (2006b) - Massachusetts Tidal In-Stream Energy Conversion (TISEC): Survey and Characterization of Potential Project Sites. EPRI-TP-003-MA. EPRI (2006c) - New Brunswick Tidal In-Stream. Energy Conversion (TISEC): Survey and Characterization of Potential Project Sites. EPRI-TP-003-NB. EPRI (2006d) - Nova Scotia Tidal In-Stream Energy Conversion (TISEC): Survey and Characterization of Potential Project Sites. EPRI-TP-003-NS. EPRI (2006e) - Tidal InStream Energy Resource Assessment for Southeast Alaska. EPRI-TP-003-AK. EPRI (2006f) - Tidal power in North America Environmental and Permitting Issues. Technical report, Devine Tarbell & Associates Inc., Electric Power Research Institutes. EPRI-TP-007-NA. Vol. 9 No. 2 pp December 2014 Marine Systems & Ocean Technology 123

54 Insight into the usage of turbine current converters on the Southern Brazilian Shelf Eduardo de Paula Kirinus; Wiliam Correa Marques and Helena Barreto Matzenauer GORDON, A. L. (1989) - Brazil - Malvinas Confluence Deep-Sea Research, 36: GORLOV, B. A. (2010) - Helical Turbine and Fish Safety. pages HARDISTY, J, (2009) The Analysis of Tidal Stream Power. The University of Hull, Kingston-upon-Hull, UK. John Wiley & Sons, Ltd. ISBN: p. HERVOUET, J. M. (2007) - Free surface Flows: Modelling with the finite element methods. HERVOUET, J. M. and Van Haren, L. (1996) - Recent advances in numerical methods for fluid flows. In ANDERSON, M. G., Walling, D. E., and Bates, P. D., editors, Floodplain processes, pages Wiley, Chichester. KALNAY, E., Kanamitsu, M., Kistler, R., Collins, W., Deaven, D., Gandin, L., Iredell, M., Saha, S., White, G., Woollen, J., Zhu, Y., Chelliah, M., Ebisuzaki, W., Higgins, W., Janowiak, J., Mo, K. C., Ropelewski, C., Wang, J., Leetmaa, A., Reynolds, R., Jenne, R., and Joseph, D. (1996) - The NCEP/NCAR 40-Year Reanalysis project. Technical report, Bulletin of the American Meteorological Society. KHAN, M. J., Bhuyan, G., Iqbal, M. T., and Quaicoe, J. E. (2009) - Hydrokinetic energy conversion systems and assessment of horizontal and vertical axis turbines for river and tidal applications: A technology status review. Applied Energy, 86(10): KIRINUS, E. P., Marques, W. C., and Stringari, C. E. (2012) - Viabilidade de conversão da energia de correntes marinhas na Plataforma Continental Sul do Brasil. Vetor, 22. KUNDU, P. K. and Cohen, I. M. (2002) Fluid Mechanics. Second Edition. Academic Press. Orlando, USA. ISBN: p. MARQUES, W. C. (2009) - Estudo da dinâmica da pluma costeira da Lagoa dos Patos. PhD thesis, Universidade Federal de Rio Grande. MARQUES, W. C. (2012) - The temporal variability of the freshwater discharge and water levels at the Patos Lagoon, Brazil. International Journal of Geosciences. MARQUES, W. C., Fernandes, E. H. L., and Moller, O. O. (2010b) - Straining and advection contributions to the mixing process of the Patos Lagoon coastal plume, Brazil. Journal of Geophysical Research, 115(C6). MARQUES, W. C., Fernandes, E. H. L., Malcherek, A., and Rocha, L. A. O. (2012) - Energy converting structures in the Southern Brazilian Shelf: Energy Conversion and its influence on the hydrodynamic and morphodynamic processes. Journal of Geophysical Research. MARQUES, W. C., Fernandes, E. H., Möller Jr, O. O., Moraes, B. C., and Malcherek, A. (2010a) - Dynamics of the Patos Lagoon coastal plume and its contribution to the deposition pattern of the southern Brazilian inner shelf. Journal of Geophysical Research, 115. MÖLLER, O. O. J., Piola, A. R., Freitas, A. C., and Campos, E. J. D. (2008) - The effects of river discharge and seasonal winds on the shelf off southeastern South America. Continental Shelf Research. MONTEIRO, I. O. (2006) - Modelagem barotrópica da pluma da Lagoa dos Patos. PhD thesis, Universidade Federal de Rio Grande. MYERS, L. E. and Bahaj, A. S. (2012) - "An experimental investigation simulating flow effects in first generation marine current energy converter arrays," Renewable Energy, vol. 37, 2012, pp PIOLA, A. R. and Matano, R. P. (2001) - Brazil and Falklands (Malvinas) currents. Piola, A. R., Matano, R. P., Palma, E. D., Moller, O. O., and Campos, E. J. (2005) - The influence of the Plata River discharge on the western South Atlantic shelf. Geophysical Research Letters, 32:L Podestá, G. P. (1997) - Utilización de datos satelitarios en investigaciones oceanográficas y pesqueras en el Océano Atlántico Sudoccidental. In BOSCHI, E. E., editor, El mar argentino y sus recursos pesqueros., pages Mar del Plata, Argentina. Smagorinski, J. (1963) General circulation experiments with the primitive equation, I. The basic experiment. Weather Review. 91, Torrence, C. and Compo, G. P. (1997) - A practical guide to wavelet analysis. Technical report, Bulletin of the American Meteorological Society. 124 Marine Systems & Ocean Technology Vol. 9 No. 2 pp December 2014

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56 MS&OT Guidelines for Authors Title of paper First Name Surname, Organisation, Address of corresponding author (including ) Abstract The abstract should be a brief description of the scope of the paper, not exceeding 100 words in length Keywords: at least 3 suitable words for indexing purposes Nomenclature A nomenclature is required for papers using a large number of symbols, abbreviations and acronyms. Where possible, these should be ordered alphabetically. Symbol 1 Definition Symbol 2 Definition etc. E.g.: α Angle of attack ρ Density of water λ Wave length 1. Introduction This is normally the first section in the main body of the text. Please note that this section and all subsequent sections and subsections are numbered. All main headings should be typed in bold as shown below. 2. Heading 2.1 Sub-heading Each Section may have sub-headings. Sub-headings should be numbered and typed using lower case as above. 2.2 Sub-heading 2.2 (a) Further subsidiary heading The sub-sections can be further divided up as above. Further subsidiary headings not in bold in lower case. 3. Manuscript format conventions 3.1 Font The fonts to be used are the same that have been used for this page, Times New Roman and Arial. The title of the paper should be in 12 point bold capitals. Authors names should be in 10 point bold, with affiliation in 10 point regular. The rest of the paper should be in 10 point using the font style indicated in this template. 3.2 Page setup The final manuscript should use the style used in this template. The margins are as follows for both A4 and US letter style in order that Acrobat versions of the manuscript can be printed on either A4 or 8.5x11 inch paper: A4 8.5x11 in. Top 2.5cm 1.0 in Bottom 3.5cm 0.7 in Left 1.7cm 0.8 in Right 3.5cm 0.7 in 126 Marine Systems & Ocean Technology

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59 SOBENA Sociedade Brasileira de Engenharia Naval The Sociedade Brasileira de Engenharia Naval (SOBENA) is the Brazilian forum for exchange of theoretical and practical knowledge amongst naval architects and marine engineers. It was founded in the beginning of the modern phase of Brazilian naval construction, in 1962, with the aim of bringing together engineers, technicians and other professionals involved in activities as: shipbuilding and ship repair, design and other engineering services, maritime transportation, waterways, ports, specialized cargo terminals, ocean and river transportation economics, marine environmental protection, offshore support bases, offshore logistics, naval aspects of offshore exploration and production, construction and conversion of platforms and other offshore vessels. SOBENA is a non-profit civil society, declared a federal public utility by Decree No /89, which since its foundation is aimed at promoting technological development in the above activities through courses, conferences, seminars, lectures and debates. SOBENA is a source of reference called upon to provide its opinion on matters of public interest and has also been politically active, expressing its views concerning topics of national relevance related to its areas of activity. Following the evolution of the industry in the past years, SOBENA has started to include activities related to offshore oil exploration and production, holding events for professionals of those areas. As a member of the Mobilizing Committee of the National Petroleum Industry Organization (ONIP), SOBENA has been taking part in various subcommittees which are seeking to create conditions to promote the development of the Brazilian naval and offshore construction industry. SOBENA has signed affiliation agreements with the Institute of Marine Engineers (IMarEST), with headquarters in London, England and cooperative agreement with The Society of Naval Architects and Marine Engineers (SNAME), from the United States of America. President Floriano Carlos Martins Pires Jr. Vice-President Luis de Mattos Regional Director - São Paulo Hélio Mitio Morishita Administrative Director João Carlos dos Santos Pacheco Financial Director Luiz Carlos de A. Barradas Filho Technical Director Murilo Augusto Vaz Regional Director - São Paulo Hélio Mitio Morishita Associated Directors André de Souza Manhães Thiago M. C. Lembruger Porto Luiz Felipe Pimentel M. de Araújo Address: Av. Presidente Vargas, Gr. 713 Centro - CEP Rio de Janeiro - RJ - Brasil Telephone: [+55](21) sobena@sobena.org.br Site: CEENO Centro de Excelência em Engenharia Naval e Oceânica The Centre of Excellence in Naval Architecture and Ocean Engineering (CEENO) was created in 1999 as a result of a joint initiative of four Brazilian institutions (COPPE, IPT, PETROBRAS and USP), traditionally involved in scientific and technological development applied to marine activities. As a Centre of Excellence, CEENO aims to integrate facilities and human resources, developing theoretical and experimental methods, giving strong support for consolidation, expansion and improvement of the maritime activities in Brazil and worldwide. CEENO has been involved in relevant projects on Offshore Engineering and Ship Design & Construction.