Vol.6, April.2014 ISSN

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1 Vol.6, April.4 ISSN

2 -Science and Engineering- Vol.6: April 4 Contents About JOMAse Scope of JOMAse Editors Title and Authors Application and Development of Multi-Hulls Pages Victor A. Dubrovsky - 7 Linearized Morison Drag for Improvement Heave Response of Semi- Submersible by Diffraction Potential Siow, C. L, Jaswar Koto, Hassan Abyn and N.M Khairuddin Energy Transmission to Long Waves Generated by Instantaneous Ground Motion on a Beach Arghya Bandyopadhyay and Avijit Mandal Study on Wave Buoy Legged Spider Power Device Priyanto, A, Maimun, A, Zamani, M, Jaswar Koto and Kader, A.S.A 4-9 Ocean and Aerospace Research Institute, Indonesia Call for Papers on Ocean, Mechanical and Aerospace Scientists and Engineers (OMAse) 4 ISOMAse International Society of Ocean, Mechanical and Aerospace -Scientists and Engineers-

3 -Science and Engineering- Vol.6: April 4 About JOMAse The Journal of Ocean, Mechanical and Aerospace -science and engineering- (JOMAse, ISSN: ) is an online professional journal which is published by the International Society of Ocean, Mechanical and Aerospace -scientists and engineers- (ISOMAse), Insya Allah, twelve volumes in a year. The mission of the JOMAse is to foster free and extremely rapid scientific communication across the world wide community. The JOMAse is an original and peer review article that advance the understanding of both science and engineering and its application to the solution of challenges and complex problems in naval architecture, offshore and subsea, machines and control system, aeronautics, satellite and aerospace. The JOMAse is particularly concerned with the demonstration of applied science and innovative engineering solutions to solve specific industrial problems. Original contributions providing insight into the use of computational fluid dynamic, heat transfer, thermodynamics, experimental and analytical, application of finite element, structural and impact mechanics, stress and strain localization and globalization, metal forming, behaviour and application of advanced materials in ocean and aerospace engineering, robotics and control, tribology, materials processing and corrosion generally from the core of the journal contents are encouraged. Articles preferably should focus on the following aspects: new methods or theory or philosophy innovative practices, critical survey or analysis of a subject or topic, new or latest research findings and critical review or evaluation of new discoveries. The authors are required to confirm that their paper has not been submitted to any other journal in English or any other language. ISOMAse International Society of Ocean, Mechanical and Aerospace -Scientists and Engineers-

4 -Science and Engineering- Vol.6: April 4 Scope of JOMAse The JOMAse welcomes manuscript submissions from academicians, scholars, and practitioners for possible publication from all over the world that meets the general criteria of significance and educational excellence. The scope of the journal is as follows: Environment and Safety Renewable Energy Naval Architecture and Offshore Engineering Computational and Experimental Mechanics Hydrodynamic and Aerodynamics Noise and Vibration Aeronautics and Satellite Engineering Materials and Corrosion Fluids Mechanics Engineering Stress and Structural Modeling Manufacturing and Industrial Engineering Robotics and Control Heat Transfer and Thermal Power Plant Engineering Risk and Reliability Case studies and Critical reviews The International Society of Ocean, Mechanical and Aerospace science and engineering is inviting you to submit your manuscript(s) to isomase.org@gmail.com for publication. Our objective is to inform authors of the decision on their manuscript(s) within weeks of submission. Following acceptance, a paper will normally be published in the next online issue. ISOMAse International Society of Ocean, Mechanical and Aerospace -Scientists and Engineers-

5 -Science and Engineering- Vol.6: April 4 Editors Chief-in-Editor Jaswar Koto (Ocean and Aerospace Research Institute, Indonesia) Associate Editors Adhy Prayitno Agoes Priyanto Ahmad Fitriadhy Ahmad Zubaydi Buana Ma ruf Carlos Guedes Soares Dani Harmanto Iis Sopyan Jamasri Mazlan Abdul Wahid Mohamed Kotb Priyono Sutikno Sergey Antonenko Sunaryo Tay Cho Jui (Universitas Riau, Indonesia) (Universiti Teknologi Malaysia, Malaysia) (Universiti Malaysia Terengganu, Malaysia) (Institut Teknologi Sepuluh Nopember, Indonesia) (Badan Pengkajian dan Penerapan Teknologi, Indonesia) (Centre for Marine Technology and Engineering (CENTEC), University of Lisbon, Portugal) (University of Derby, UK) (International Islamic University Malaysia, Malaysia) (Universitas Gadjah Mada, Indonesia) (Universiti Teknologi Malaysia, Malaysia) (Alexandria University, Egypt) (Institut Teknologi Bandung, Indonesia) (Far Eastern Federal University, Russia) (Universitas Indonesia, Indonesia) (National University of Singapore, Singapore) Published in Indonesia. Printed in Indonesia. JOMAse ISOMAse, Jalan Sisingamangaraja No.89 Pekanbaru-Riau Indonesia Teknik Mesin Fakultas Teknik Universitas Riau, Indonesia ISOMAse International Society of Ocean, Mechanical and Aerospace -Scientists and Engineers-

6 April, 4 Application and Development of Multi-Hulls a) Balt Techno Prom, St.Petersburg, Russia Victor A. Dubrovsky, a,* *Corresponding author: multi-hulls@yandex.ru Paper History Received: 8-January-4 Received in revised form: 5-February-4 Accepted: 8-March-4 ABSTRACT A brief history of the expanded application of multi-hull ships and boats is shown. The possibilities of catamaran development are proposed. The first line of multi-hull development is the wider use of various types of multi-hulls. The second line of development is a special method of designing, including complex comparison of seaworthiness. The proposed method ensures the elimination of the disadvantages of multi-hulls, and the fullest realization of their advantages. Practical examples of the developments are shown. KEY WORDS: Multi-hull Ship; Small Water-plane Ship; Twin-hull Ship; Triple-hull Ship, Catamaran, Trimaran; Outrigger Ship; Proa; Duplus; Trisec; Semi-submerged Rig. NOMENCLATURE API Δ Δ American Petroleum Institute Temperature Difference in and out Thermal Expansion Anchor Length Expansion Pressure Force Friction Force Design Compressive Strain Critical Strain. INTRODUCTION The expanded use of twin-hull ships with identical hulls of usual shape, so-called catamarans, in the trade and auxiliary fleets began after World War II. Expanded scientific programs on multi-hulls in general began at the same time. The building of semi-submersible rigs for drilling at sea also began at approximately the same time. New ships, consisting of a central main hull and one or two added side hulls (outriggers), have been built since the last quarter of the last century. Full-scale tests, wide research and practical applications of small water-plane ships also began in the last decades of the twentieth century. A new stage of application was the building of battle multihulls, and their inclusion in the naval forces of various countries. For example, wave-piercing catamarans used as missile boats were built in China; a fast catamaran for use as a corvette, and (after building and testing of an experimental ship Triton in the UK) fast outrigger combat ships were built in the USA. Today there is a large amount of full-scale, experimental and theoretical experience of research into various multi-hulls. This experience allows wider and more effective application of such ships for various purposes.. The Main Results of Practical Applications. A large number of multi-hulls have been built since the middle of the twentieth century: Thousands of small-sized ships and boats for uses including passenger, tourist, pleasure, and fishery roles; - Hundreds of catamarans as fast passenger and carpassenger ferries (today about 7% of these ferries are catamarans); - Hundreds of semi-submersible rigs for various purposes; - Dozens of small water-plane area ships for full-scale tests and for practical applications; - A number of ships with one or two outriggers, including a record sail racer. Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

7 April, 4 Evidently, some types of multi-hulls are applied: - The catamarans as are most spread type; - The twin-hull ships with small water-plane area, so named dupluses ; - Some ships with outriggers and usually shaped main hull. A more detailed description of the history and state of the art of multi-hulls can be found in the monograph []. The science and practical results are contained in [], [3]. The characteristics of the multi-hulls in use today are briefly examined below. The relatively larger area of their decks, elimination of the transverse stability problem, reduced roll, the major provision of non-sinkability, and the large aspect ratio of the hulls, all ensure the effective application of catamarans as fast passenger and carpassenger ferries. Today the special shape of the bow parts of the hulls and the above-water platform ensures the highest level of seakeeping in head waves in the so-called wave-piercing catamarans (WPC). Such catamarans are the most effective ferries in terms of contemporary capacity and speed, Fig.. The high transverse stability and the large area of the upper decks are major advantages of catamarans used as a sea-going cranes or crane ships. The simple modernization of any monohull by adding one or two outriggers allows a substantial increase of capacity (on the decks) and transverse stability, i.e., greater safety of ships employed for various purposes, such as passenger transport or fishery. This modernization can be carried out even without docking the initial ship. The building of an outrigger battleship is the next important stage of naval fleet development. Such a ship differs from a comparable monohull in having a larger area upper deck, greater transverse stability, a larger aspect ratio of the main hull (with the usual shape), and smaller pitch at moderate speeds, Fig.. Semi-submersible rigs, as floating objects with a small waterplane area, consist of two or three underwater pontoons that are connected with the above-water platform by a number of struts built in rectangular or circular sections (columns). The design draft is placed at about half of the column height, while the transport draft is placed near the top of the pontoons. Such rigs guarantee all-weather exploitation even in the worst wave and wind conditions. A separate line of multi-hull development today is researching and building high-speed ships with a small water-plane area and twin hulls (SWATH - ship with small water-plane, twin hull ). A lot of theoretical, full-scale and experimental data shows that the seaworthiness of a SWATH is approximately the same as that of a monohull with a bigger (5-5 times greater) displacement. The other specificities of SWA ships are the same as those of other multi-hulls: increased area of decks, large volume of the above-water platform, lack of transverse stability problems. Figure : A typical wave-piercing catamaran. Figure : The outrigger battle ship of US Navy. Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

8 April, 4.. BIG FAMILY OF MULTI-HULLS. Today there are the theoretical and experimental data on the characteristics of a bigger, than applied, line of multi-hulls. For example, Fig. 3 shows the researched types of multihulls of usual shape of hulls. Figure 3: Some examined types of usually-shaped multi-hulls:, the catamarans with symmetrical and unsymmetrical hulls (the biggest transverse stability); 3,4 the same trimarans (in Russian terminology), the biggest interaction of wave systems; 5 a catamaran with shifted hulls (a sum of characteristics of a catamaran and a trimaran); 6 proa (the minimal mass of the transverse structure); 7 an outrigger ship (small enough mass of transverse structure). Fig. 4 contains some types of ships with small water-plane area (SWA ships). outriggers (option of S.Rudenko); 6 foiled monohull SWA ship, for higher achievable speeds. Table shows the main difference of any multi-hulls^ relative bigger area of (upper) deck. In general, the existing experience of multi-hull researching shows the following characteristics: - increased area of decks (and corresponding possible growth of inner volume); - better performance (at medium and high relative speeds) by reason of the high aspect ratio of the hulls; - generally better seaworthiness (compared with monohulls with the same displacement); - any required transverse stability without any restriction of the aspect ratio of hulls; - increased above-water volume, which can be watertight and can be divided by watertight bulkheads; - possibility of the design draft decreasing without loss of seakeeping. In addition, SWA ships can have a minimal draft while in harbor, as well as greater draft at sea (for better seaworthiness) by means of relatively small water ballast. - However, the same experience also shows the common disadvantages of multi-hulls: - relatively larger wetted area, which means worse performance at low relative speeds; - greater mass of hull structures relative to the displacement; - a substantial possibility of wet deck slamming in head waves; - increased overall width. More detailed comparison of the monohull and some multihulls are shown by the Table. It must be noted that several types of multi-hulls are currently being researched [], [], [3]; all of these differ from each other and from the monohulls in various stages. The application of other types of multi-hulls is the first line of development. 3.. CATAMARAN DEVELOPMENTS Unfortunately, the development of all the technical characteristics as a whole is impossible. Therefore, the previously shown features of ship types allow the development of the most important (for the required purpose) characteristics of a catamaran. Figure 4: Some examined ships with small water-plane area: a duplus (twin-hull ship with one long strut on each under-water volume, gondola ), maximal transverse stability of SWA ships; a trisec (twin-hull ship, two short struts on each gondola) minimal area of water-plane; 3 a tricore (triple-hull ship of small water-plane area), maximal interaction of wave systems of SWA ships; 4 an outrigger SWA ship, small enough mass of the transverse structure; 5- a ship with usual main hull and SWA 3.. Increased Seaworthiness This can be achieved by a transition from the catamaran to the duplus if smaller transverse stability and lower achievable speed are permissible. Table 3 contains a comparison of the achievable (from the vertical acceleration point of view) speed in head waves of two ships with t displacement and equal installed power, and no motion mitigation. The estimations are based on test results in the seakeeping basin of the Krylov Shipbuilding Research Centre, Russia. The advantage of the small-sized duplus is clear: the corresponding catamaran can ensure a minimal speed only at Sea State 3. Fig. 5 contains an example of the achievable speeds in head waves of two,-t ships, for bow acceleration level a/g =.4. 3 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

9 April, 4 Table : Relative deck area comparison, (here: L, L - length of the initial (combat) monohull and a hull of the comparable multi-hull; L OA - overall length of a multi-hull, V volume displacement of the monohull; B, B, B OA beam of the initial monohull, beam of a hull of comparable multi-hull, overall beam of a multi-hull; A UD - upper deck area coefficient). Ship type Relative length of a hull Most possible dimensions Monohull l MON =L/V /3 L/B=8; A UD ~.8.*L Relative area of upper deck Catamaran l = l MON L =.8*L; B =.8*B; A UD ~.9; B OA =(4 8)B (.3.46)*L Duplus or trisec l =.8*l MON L =.64*L; B OA =(.3.5)*L ;A UD ~. (.9.3)*L Outriggered usual hull l =.*l MON L /B =; L OA =(.3.4)*L ; B OA =(..3)*L ; (.7.5)*L Outriggered SWA hull l =.8*l MON L =.8*L; Lo=(.3.4)*L ; B OA =(.3.5)*L ; (.8.3)*L Tricore l =.5*l MON L =.35*L; L OA =.6*L ; B OA =(.6.8)*L ; (.8.)*L Trimaran (Russian understanding) l =.6*l MON L =.4*L; L OA =.6*L ; B OA =(.4.5)*L ; (.9.)*L Table : The main advantages and disadvantages of different types of displacement ships. Type Advantages Disadvantages Monohull Most comprehensively studied and most commonly used. Lowest building cost per ton of displacement. Minimal relative wetted area. Limited initial stability for slender hulls. Speed or heading on rough seas is limited by roll and pitch motions, slamming, green water and longitudinal Catamaran SWATH Ship with conventional main hull and two outriggers Ship with SWA main hull and two outriggers. Lowest building cost per square meter of decks. No problems with initial stability and rolling. Vehicles can be conveniently placed far above WL. Lower wave resistance. Lower probability of bottom slamming. Wide and well elevated deck area for vehicles. Perfect initial stability, roll and pitch motions. Low longitudinal bending moment; it drops at higher speed in head seas. Low wave resistance. Low slamming probability. Low additional resistance in waves. Wide and convenient cargo deck well above WL. Satisfactory initial transverse stability. Lower, than for monohull, wave resistance of main hull. Lower probability of bottom slamming. Transverse bending moment is less than that for catamaran and SWATH Wide and convenient cargo deck well above WL. Satisfactory initial transverse stability. Low transverse bending moment. Low wave resistance. Good motions and no slamming. Low additional resistance bending moment. Wide overall beam. Higher weight of metal structure per ton of displacement. Larger relative wetted area. Speed or heading on rough seas are limited by pitch, slamming of wet deck, and longitudinal bending moment. Wide overall beam, transverse bending moment is greater than for catamaran. Greater relative wetted area. Narrow struts and gondolas make it difficult to place and access the main engines. Greater relative wetted area. Wider, than for monohull, overall beam, larger relative wetted area. Higher, than for monohull, longitudinal bending moment, which rises in higher seas. For stern outriggers worse controllability, than that of a monohull,. Large overall beam. Wetted area is greater than for conventional main hull. For outriggers place aft, controllability is worse. The least apprehended yet and novel concept. Table 3.The achievable speeds of two -t ships in head waves (the various vertical accelerations at bow, a/g ). Sea State Catamaran, a/g =.5, knots 3 3 The same ship, a/g = Duplus, a/g =.5, knots The same ship, a/g = Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

10 April, 4 Achievable speed, kn 6 5 SWATH advantages. For example, the pulling propellers ensure a minimal level of underwater noise for ships which require that characteristic. For example, Fig. 7 shows an external view of an outrigger seismic ship as an alternative to the catamaran used for the same purpose. 4 3 Semi-planing monohull W ave height of 3-% occurence, m Figure 5: The achievable speeds in head waves,, t, a/g=.4. It must be noted that any motion mitigation is very effective for SWA ships, because they differ in their decreased disturbing forces and moments, compared with those generated by motion mitigation devices. 3.. Better Performance at the Defined Range of Speeds The favorable interaction of the wave systems which are generated by a trimaran (in the Russian sense: a triple-hull ship built with identical traditional hulls) is greatest at the Froude numbers for a hull length from.4 to.7, with the maximum near.5. This means a substantially better performance is possible if a catamaran is replaced by a trimaran (see Fig. 6). Figure 7: General arrangement of the seismic ship with a minimal level of under-water noise Growth of Achievable Speed As noted previously, today s wave-piercing catamarans (WPCs) are the best fast vessels because of their good performance at high speeds, satisfactory seaworthiness and not so high cost of building. But most fast WPCs have a relative speed on the higher level of the transient speed regime. Their higher speed needs changing the shape of the hulls; instead of the lengthened smooth hulls of a catamaran, sharp hulls with a small aspect ratio are needed for the planning regime. A new type of super-fast vessel has been proposed, called the wave-piercing trimaran (WPT). Fig. 8 shows a comparison of the installed power of two WPCs with two corresponding WPTs. The WPTs clearly perform better at approximately twice the speed of the WPCs. Power, thou. hp. 8 6 Catamaran, 5 t WPT, 5 t. 4 Catamaran. t. 8 6 WPT, t. 4 Figure 6: The power comparison of the catamaran and two trimaran options, displacement 5 t. It is clear that the installed power of the better trimaran can be 3-35% less than that of the catamaran Decreased Hull Structure Mass If the inner volume of the above-water platform is constant, the transition from a catamaran type to an outrigger type allows some reduction of the hull structure mass. Moreover, in some cases, an outrigger ship has other Speed, kn Figure 8: Power comparison of two WPCs and corresponding WPTs. Tests on the models have shown the dynamic stability of a WPT in the vertical plane up to a relative speed (Froude number by hull displacement) of up to 7.5. In addition, the possibility of bottom slamming of sharp hulls is very low.fig. 9 shows an example of the WPT as a passenger ferry ( t, -5 passengers, up to knots). 5 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

11 April, The hull mass is estimated on the basiss of the preliminary series of calculations; The seakeeping comparison by only one number, which means the possibility of fulfilling the required seakeeping standards. The proposed algorithm is shown in Fig.. Figure 9: WPT as a ferry, up to knots. 4. THE DEVELOPMENT OF AN OUTRIGGERR SHIP. The methods of outrigger ship development are defined by the needs of the owner and/or operator. The following aims and methods are possible: - For improved seaworthiness replacing the traditional main hull by a hull with a small water-plane area; - For better performance at moderate speeds replacing the outrigger ship with a triple-hull ship with identical (traditional or small-water plane) hulls. Figure : The specific algorithm for dimension selection. Fig. shows an example of the application of the proposed algorithm for designing a passenger outrigger ship. Figure : A comparison of the middles: left dimensions selected by an intuitive method; final displacement 6, t; right dimensions selected by the proposed method; final displacement 4,5 t. The proposed method has been the main basis of many of the proposed conceptions of multi-hullof some of the proposed concepts. for various purposes. Fig. gives examples 5.. THE DEVELOPMENT OF SWA SHIPS Some methods of SWA ship development are described in [3]. For example, as for a catamaran, the better performance of a duplus can be ensured by the transition to a tricore (triple-hull SWA ship with the identical hulls), if the Froude number by a tricore hull length is near.5. A special shape of hull can ensure the achievable speed of a SWA ship near the planning regime of speed (a so-called semi-submersible SWA ship). Moreover, all SWA ships can have a smaller overall draft and greater damping of motions if the gondolas are designed with their height half that of the beam. - For seaworthiness replacing the traditional under-water volume ( gondola) of circular frames by the gondolas of elliptical frames with its height is equal to half of its beam; - For better performance at moderate speeds replacing the outrigger ship with a triple-hull ship with identical (small- water plane area) hulls. 6. THE DEVELOPMENT OF THE DESIGN ALGORITHM. A specially designed algorithm is the second method used in multi-hull development. The algorithm includes the following components compared with the usual design methods: - The required area of the decks (or inner volume) is one of the main initial data for dimension selection; - The main technical characteristics are defined by variant calculations (because the multi-hulls do not usually have any design prototypes); 6 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

12 April, 4 cabins and saloons, wheeled vehicles, science laboratories, compartments for weapon systems, etc. However, the big family of multi-hulls can ensure some essential developments of characteristics for various purposes. It is therefore recommended that there should be wider application of various types of multi-hulls, and the use of the special algorithm in their design. REFERENCES Figure: Some new concepts of multi-hulls proposed by the author. 7. CONCLUSIONS AND RECOMMENDATIONS The brief history of multi-hulls since the middle of the twentieth century shows their expanded application for the transportation of volume relatively light cargo, such as passengers in the. Dubrovsky, V., Lyakhovitsky, A., Multi-hull ships,, Backbone Publishing Co., Fair Lawn, USA, 495 p.. Dubrovsky, V., Ships with outriggers, 4, Backbone Publishing Co., Fair Lawn, USA, 88 p. 3. Dubrovsky, V., Matveev, K., Sutulo, S., Small water-plane area ships, ISBN , Hoboken, USA, 56 p. 4. Multi-hull ships, ed. V. Dubrovsky, 978, Sudostrojenije Publishing House, Leningrad, USSR [in Russian]. 7 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

13 April, 4 Linearized Morison Drag for Improvement Semi-Submersible Heave Response Prediction by Diffraction Potential Siow, C. L, a, Jaswar Koto, a, b,*, Hassan Abyn, a and N.M Khairuddin, a a) Aeronautical, Automotive and Ocean Engineering, Universiti Teknologi Malaysia, Malaysia b) Ocean and Aerospace Research Institute, Indonesia *Corresponding author: jaswar.koto@gmail.com Paper History Received: -March-4 Received in revised form: 3-April-4 Accepted: -April-4 ABSTRACT This research is targeted to improve the semi-submersible heave response prediction by using diffraction potential theory by involving drag effect in the calculation. The comparison to the experimental result was observed that heave motion tendency predicted by the diffraction potential theory is no agreed with motion experimental result when the heave motion is dominated by damping. In this research, the viscous damping and drag force for heave motion is calculated from the drag term of Morison equation. The nonlinear drag term in Morison equation is linearized by Fourier series linearization method and then inserted into the motion equation to correct the inadequate of diffraction potential theory. The proposed numerical method is also applied to simulate the semi-submersible motion response to obtain the heave motion tendency predicted by this numerical method. In comparison to the experimental result which tested at the same wave condition obtained that the diffraction potential theory with the Morison drag term correcting is able to provide satisfying heave response result especially in damping dominated region. KEY WORDS: Morison Equation, Diffraction Potential Theory, Semi-submersible, Motion Response, Viscous Damping.. INTRODUCTION This work is targeted to propose a correction method which applicable to linear diffraction theory in order to evaluate the motion response of selected offshore floating structure. The linear diffraction theory estimate the wave force on the floating body based on frequency domain and this method can be considered as an efficient method to study the motion of the large size floating structure with acceptable accuracy. The effectiveness of this diffraction theory apply on large structure is due to the significant diffraction effect exist on the large size structure in wave [7]. However, some offshore structure such as semi-submersible, TLP and spar are looked like a combination of several slender bodies as an example, branching for semi-submersible. In this study, semi-submersible structure is selected as an offshore structure model since this structure is one of the favours structure used in deep water oil and gas exploration area. To achieve this objective, a programming code was developed based on diffraction potential theory and it is written in visual basic programming language. By comparing the numerical result predicted by using diffraction potential theory to experiment result, it is obtained that the motion prediction by diffraction potential theory has an acceptable accuracy mostly, except for heave motion when the wave frequency near to the structure natural frequency [8, 9]. As presented in a previous paper, the diffraction potential theory is less accurate to predict the structure heave motion response when the wave frequency closer to structure natural frequency. At this situation, the heave response calculated by the diffraction potential theory will be overshooting compare to experiment result due to low damping executed by the theory and then follow by the large drop which give and underestimating result compare to experiment result before it is returned into normal tendency [8]. In order to correct the over-predicting phenomenon made by the diffraction potential theory, the previous research was trying to increase the damping coefficient by adding viscous damping into the motion equation [9]. From that study, the viscous damping is treated as extra matrix and added into the motion equation separately. This addition viscous damping was estimated based on the equation provided by S. Nallayarasu and P. Siva Prasad in their published paper []. 8 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

14 April, 4 By adding the extra viscous damping into the motion equation, it can be obtained that the significant over-predicting of heave motion when wave frequency near to the floating structure natural frequency was corrected and it is close to the experimental result compared to executed result by diffraction potential theory alone [9]. However, the under-predicting of the heave response by diffraction potential theory in a certain wave frequency region still remaining unsolved by adding the viscous damping to the motion equation as discussed in the previous study [9]. In this paper, the discussion will focus on the effect drag force and viscous damping in estimate the semi-submersible heave response using diffraction potential theory. To able the numerical solution to calculate the extra drag force and viscous damping, the drag term in Morison equation is applied here. Accuracy of this modification solution also checked with the previous semisubmersible experiment result which carried out at the towing tank belongs to Universiti Teknologi Malaysia [, 8]. The experiment is conducted in head sea condition and slack mooring condition for wavelength around meter to 9 meters. In the comparison, it is obtained that the non-agreed heave response tendency near the structure natural frequency predicted by diffraction potential theory can be corrected by involving the drag effect in the calculation.. LITERATURE REVIEW Hess and Smith, Van Oortmerssen and Loken studied on nonlifting potential flow calculation about arbitrary 3D objects [,, 3]. They utilized a source density distribution on the surface of the structure and solved for distribution necessary to lake the normal component of fluid velocity zero on the boundary. Plane quadrilateral source elements were used to approximate the structure surface, and the integral equation for the source density is replaced by a set of linear algebraic equations for the values of the source density on the quadrilateral elements. By solving this set of equations, the flow velocity both on and off the surface was calculated. Besides, Wu et al. also studied on the motion of a moored semi-submersible in regular waves and wave induced internal forces numerically and experimentally [4]. In their mathematical formulation, the moored semi-submersible was modelled as an externally constrained floating body in waves, and derived the linearized equation of motion. Yilmaz and Incecikanalyzed the excessive motion of moored semi-submersible [5]. They developed and employed two different time domain techniques due to mooring stiffness, viscous drag forces and damping. In the first technique, first-order wave forces acting on structure which considered as a solitary excitation forces and evaluated according Morison equation. In second technique, they used mean drift forces to calculate slowly varying wave forces and simulate for slow varying and steady motions. Söylemez developed a technique to predict damaged semi-submersible motion under wind, current and wave [6]. He used Newton s second law for approaching equation of motion and developed numerical technique of nonlinear equations for intact and damaged condition in time domain. Clauss et al. analyzed the sea-keeping behavior of a semisubmersible in rough waves in the North Sea numerically and experimentally [7]. They used panel method TiMIT (Timedomain investigations, developed at the Massachusetts Institute of Technology) for wave/structure interactions in time domain. The theory behind TiMIT is strictly linear and thus applicable for moderate sea condition only. An important requirement for a unit with drilling capabilities is the low level of motions in the vertical plane motions induced by heave, roll and pitch. Matos et al. were investigated second-order resonant of a deep-draft semi-submersible heave, roll and pitch motions numerically and experimentally [8]. One of the manners to improve the hydrodynamic behavior of a semi-submersible is to increase the draft. The low frequency forces computation has been performed in the frequency domain by WAMIT a commercial Boundary Element Method (BEM) code. They generated different number of mesh on the structure and calculated pitch forces. Due to the complexity of actual structures hull form, S. Nallayarasu and P. Siva Prasad were used experimental and numerical software (ANSYS AQWA) to study the hydrodynamic response of an offshore spar structure which linked to semisubmersible under regular waves. From both the experimental and numerical result, it is obtained that the response of the spar is reduced after linked to semi-submersible due to the interaction of radiation wave generated by both the structures and the motion of spar may be reduced by semi-submersible. However, the research also obtained that the motion response for unmoored semisubmersible is increased when linked to spar []. Wackers et al. was reviewed the surface descretisation methods for CFD application with different code [9]. Besides, simulation of fluid flow Characteristic around Rounded-Shape FPSO was also conducted by A. Efi et al. using RANs Method []. Jaswar et al. were also developed integrated CFD simulation software to analyze hull performance of VLCC tanker. The integrated CFD simulation tool was developed based on potential theory and able to simulate wave profile, wave resistance and pressure distribution around ship hull []. In addition, few experiment tests were carried out to obtain the motion response of semi-submersible. A model test related to interaction between semi-submersible and TLP was carried out by Hassan Abyn et al. []. In continue Hassan Abyn et al. also tried to simulate the motion of semi-submersible by using HydroSTAR and then analyse the effect of meshing number to the accuracy of execution result and execution time [3]. Besides, C. L. Siow et al. also make a comparison on the motion of semi-submersible when it alone to interaction condition by experimental approach [4]. Besides that, K.U. Tiau () was simulating the motion of mobile floating harbour which has similar hull form as semisubmersible by using Morison Equation [5]. In addition, C. L. Siow et.al also examined the heave damping efficiency for semisubmersible calculated by the diffraction potential theory at the damping dominate region and then they also propose an viscous damping correction method to increase the heave damping to improve the numerical result [9]. 3. MATHEMATICAL MODEL 3. Diffraction Potential In this study, the diffraction potential method was used to obtain the wave force act on the semi-submersible structure also the added mass and damping for all six directions of motions. The regular wave acting on floating bodies can be described by 9 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

15 April, 4 velocity potential. The velocity potential normally written in respective to the flow direction and time as below: Φ,,,, (),,,,,,,, () where; g is gravity acceleration, is incident wave amplitude, is motions amplitude, is incident wave potential, is scattering wave potential, is radiation wave potential due to motions and is direction of motion. From the above equation, it is shown that total wave potential in the system is contributed by the potential of the incident wave, scattering wave and radiation wave. In addition, the phase and amplitude for both the incident wave and scattering wave is assumed to be the same. However, radiation wave potentials are affected by each type of motions of each single floating body inside system, where the total potential for radiation wave for the single body is the summation of the radiation wave generates by each type of body motions such as roll, pitch, yaw, surge, sway and heave. Also, the wave potential must be satisfied with boundary conditions as below: (3) (4) (5) ~ (6) (7) 3. Wave Potential By considering the wave potential only affected by structure surface, S H, the wave potential at any point can be presented by the following equation: ; ; (8) where P =(x, y, z) represents fluid flow pointed at any coordinate and,, represent any coordinate, (x, y, z) on structure surface, S H. The green function can be applied here to estimate the strength of the wave flow potential. The green function in eq. (8) can be summarized as follow: ; 4,, where,, in eq. (9) represent the effect of free surface and can be solved by second kind of Bessel function. (9) 3.3 Wave Force, Added Mass and Damping The wave force or moment act on the structure to cause the motions of structure can be obtained by integral the diffraction wave potential along the structure surface.,, () where, is diffraction potential, The added mass, A ij and damping, B ij for each motion can be obtained by integral the radiation wave due to each motion along the structure surface.,, (),, () in eq. () to eq. () is the normal vector for each direction of motion, i = ~ 6 represent the direction of motion and j = ~6 represent the six type of motions. 3.4 Drag Term of Morison Equation The linear drag term due to the wave effect on floating structure is calculated using Drag force equation as given by Morison equation: (4) where is fluid density, is projected area in Z direction, is drag coefficient in wave particular motion direction, is velocity of particle motion at Z-direction in complex form and is structure velocity at Z-direction In order to simplify the calculation, the calculation is carried out based on the absolute velocity approach. The structure dominates term is ignored in the calculation because it is assumed that the fluid particular velocity is much higher compared to structure velocity. Expansion of the equation (4) is shown as follows: (5) (5) By ignoring all the term consist of, equation (5) can be reduced into following format. (6) The above equation (6) is still highly nonlinear and this is impossible to combine with the linear analysis based on diffraction potential theory. To able the drag force to join with the diffraction force calculated with diffraction potential theory, the nonlinear drag term is then expanded in Fourier series. By using the Fourier series linearization method, equation (6) can be written in the linear form as follow: Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

16 April, 4 (7) where, in equation (7) is the magnitude of complex fluid particle velocity in Z direction. From the equation (7), it can summarize that the first term is linearize drag force due to wave and the second term is the viscous damping force due to the drag effect. According to Christina Sjöbris, the linearize term in the equation (7) is the standard result which can be obtained if the work of floating structure performance at resonance is assumed equal between nonlinear and linearized damping term []. The linearized drag equation as shown in equation (7) now can be combined with the diffraction term which calculated by diffraction potential theory. The modified motion equation is shown as follows: (8) where is mass, is restoring force,,, is heave added mass, heave diffraction damping coefficient and heave diffraction force calculated from diffraction potential method respectively. is the viscous damping and is the drag force based on drag term of Morison equation. 3.5Differentiation of Wave Potential for Morison Drag Force To obtain the drag force contributed to heave motion, the wave particle velocity at heave direction must be obtained first. This water particle motion is proposed to obtain from the linear wave potential equation. From the theoretical, differential of the wave potential motion in Z-direction will give the water particle motion in the Z-direction. As mentioned, the drag force in Morison equation is in the function of time; therefore, the time and space dependent wave potential in the complex should be used here. The wave potential in Euler form as follows:,, (9) The expending for the equation (9) obtained that,, cos sin cos sin () Rearrange the equation (), the simplify equation as follows,, cos sin () Differentiate the equation () to the Z-direction, the water particle velocity at Z-direction is shown as follows:,, cos sin () Since this numerical model is built for deep water condition, hence it can replace the equation by and the equation () is becoming as follow:,, cos sin (3) In the equations (9) to (3), is the wave amplitude, is the gravity acceleration, is the wave speed, is wave number, is the horizontal distance referring to zero coordinate, is the time dependent variable. The horizontal distance, and the time dependent variable, can be calculated by the following equation cos sin (4) (5) In equation (4) and equation (5), the variable is wave heading angle, is the leading phase of the wave particle velocity at the Z-direction and is time. To calculate the drag forces by using the Morison equation, equation (3) can be modified by following the three assumptions below. First, since the Morison equation is a two dimensional method, therefore the projected area ofthe Z-direction is all projected at the bottom of the semi-submersible. Second, as mentioned in the previous part, this method applies the absolute velocity method and the heave motion of semisubmersible is considered very small and can be neglected; therefore, the change of displacement in Z-direction is neglected. Third, by applying the concept of oscillation motion; we can obtain that the maximum speed will occur at minimum displacement. Hence, the maximum speed and the maximum. displacement are always different by the angle From the first and second assumption, the variable at equation (3) is no effected by time and it is a constant and equal to the draught of the structure. Also, using the third assumption, it can be assumed that the leading phase for the water particle velocity at Z-direction is always a constant and have the value of. Finally, by apply the trigonometry function where cos sin and sin cos, then the equation (3) can be become as follow:,, sin cos (6) 3.6 Determination of Drag Coefficient Typically the drag coefficient can be identified from experimental results for the more accurate study. In this study, the drag coefficient is determined based on previous empirical data. To able the previous empirical used in this study, the pontoon for this semi-submersible is assumed as a horizontal cylinder. By referring to the most of the Fluid Mechanic book, it is obtained that the drag coefficient, for the cylinder with different aspect ratio,,, as shown in figure in laminar flow condition is given as in table. X Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

17 April, 4 Z Y Flow direction, U z Figure : Horizontal Cylinder and flow direction. Table : Drag Coefficient for Horizontal Cylinder [6]: Aspect Ratio, Drag Coefficient, AR,, >. The sample of pontoon for this semi-submersible is shown as follow. Figure : Isometric view for semi-submersible pontoon. To obtain the aspect ratio for this pontoon, an imaginary radius for the non-round shape pontoon should be obtained as shown in figure 3. As shown in figure 3, the imaginary radius for the semisubmersible cross section can be calculated by following equation of the depth and breadth for the pontoon is known. (7) Finally, the aspect ratio for the pontoon of semi-submersible for the flow acting in Z-direction can be obtained from the following equation Pontoon length, L (8) where L is the overall pontoon length and R is pontoon imaginary cross section radius calculate by equation (4) Figure 3: Front view for semi-submersible pontoon where R= Imaginary radius, d = Pontoon Depth, b = pontoon Breadth. 4. MODEL PARTICULAR As mentioned, the semi-submersible model was selected as the test model in this study. This Semi-submersible model was constructed based on GVA 4. The model has four circular columns connected to two pontoons and two braces. Two pieces of plywood are fastened to the top of the Semi-submersible to act as two decks to mount the test instruments. The model was constructed from wood following the scale of :7 (Table ). Upon the model complete constructed, few tests were carried out to obtain the model particulars. Inclining test, swing frame test, oscillating test, decay test and bifilar test were carried out to identify the hydrostatic particular for the semi-submersible. The dimension and measured data for the model was summarized as in table. Table : Principal particular of the Structures Length.954 m Width.835 m Draft.39 m Displacement.435 m 3 Water Plan Area.88 m Number of Columns 4 Pontoon length.954 m Pontoon depth.9 m Pontoon width.9 m Pontoons centerline separation.645 m Columns longitudinal spacing (centre).6543 m Column diameter.586 m GM T.4 m GM L.58 m K XX.45 m K YY.385 m.5 m K ZZ 5. NUMERICAL SOLUTION SETUP In this study, the numerical method applies to execute the motion response of semi-submersible will only estimate the wave force acting on the surface of the port side structure of semi- Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

18 April, 4 submersible. After that, the total wave force for the semisubmersible is double before it fixed into the motion equation. The selected semi-submersible model in this study is constructed based on GVA 4 type. Total panels used in the execution are 7 where 5 panels on each column and panels on pontoon surface. The sample of mesh constructed by this numerical method for this semi-submersible model is shown in fig.4. As similar with other diffraction potential method, this numerical method starts with mesh generation and then execute the normal vector, centre point of each panel and area for each panel. After that, the program will construct matrix element for distribution of sources and normal dipoles over the panel. Next, wave force on each panel will executed by using green function and Bessel function. At this moment, radiation force and diffraction will be considered. After that, the total wave force acting on the structure to cause the motion can be obtained by summing up the total diffraction force on each panel. At the same time, added mass and damping of the structure at same wave condition can be obtained by summing up the real part of radiation potential and imaginary part of radiation potential. If the drag term correction for heave motion is required, then the drag force and viscous damping for this motion will be executed based on the method explained in part 3.3. The required information used for the drag force calculation such as the structure offset, hydrostatic particular, wave data are same with the diffraction potential method. Calculated drag force and viscous damping are then stored in extra matrix independently before it is added to the motion equation follow the vector summation method. Lastly, the structure motion and its response to the wave can be obtained by solving the coupled motion equation. Figure 4: meshing for semi-submersible model. 6. RESULTS AND DISCUSSION The previous study obtained that the diffraction potential theory is weak in predicting the heave motion response when the wave frequency close to the structure natural frequency [8]. By detail study of the problem, it is obtained that the linear damping predicted by the diffraction potential theory is very small at the wave condition and this caused the theory to give the infinite response at the wave condition [9]. Besides, the wave force at the wave frequency around the structure natural frequency predicted by the diffraction theory also obtained small and lead to the wrong prediction of heave response if compared to experiment result. In the diffraction potential theory, the force acting on the structure is obtained by integrating the pressure distributes of the structure surface and the force is acting in the direction of the surface normal vector. The surface will contribute to the heave motion for semi-submersible structure is located at the top side of the pontoon and the bottom side of the pontoon. When the wave frequency near to the structure natural frequency, it is obtained that the wave force acting on the top side of the pontoon is nearly same to the wave force acting on the bottom side of the pontoon. This phenomenon caused the cancellation of heave force and then leads to small response predicted on this wave condition. 6. Heave Damping In this part, the discussion on heave motion response will focus on the effect of extra drag term to the motion equation and the calculated heave response amplitude operator. The damping coefficient and the heave force calculated by both the method will be first presented before the heave motion response calculated by this proposed method. The figure 5 shown the non-dimensional heave damping calculated by diffraction potential theory, Morison drags term and summation of both the heave damping by both the method. From the comparison, it is obtained that the heave damping calculated by both the method is same for wavelength under.5 meters. After wavelength equal to.5 meters, it is obtained that the damping coefficient calculated by the diffraction potential theory decrease significantly and reduced to nearly zero after wave length 5 meters. From the study, the region where the heave motion dominates by damping term is at the location where the wave frequency is close to the structure natural frequency []. Due to the small prediction of the heave damping by diffraction potential theory, the motion response calculated in this region is becomes significantly large and no agreed to the experiment result. On the other hand, the heave viscous damping calculated by the Morison drags term is keep increasing for wavelength longer than.5 meters. The heave damping predicted by the Morison drag term is predicted will become a constant if the wavelength becomes significant long as presented in figure 5. The opposite of the damping tendency between both the theories can be helped to correct the total damping value calculated from different methods. To obtain the total damping for semi-submersible heave motion, the magnitude of damping coefficient is assumed can be directly sum up for the damping calculated by both the methods. As shown in figure 5, the total damping by sum-up the damping between the two methods will be influenced by the damping coefficient calculated by two of the methods for the wavelength below 5 meters. However, due to the damping calculated by diffraction potential theory for this semi-submersible is trending to become zero for wavelength longer than 5 meters, then the tendency of total damping will be followed the tendency of the viscous damping calculated by the Morison drag term. At understood, the heave motion dominated by damping term is falling in the structure natural frequency region. For this selected structure, it is obtained that the natural frequency of heave motion is located at a wavelength around 9 meters. By referring to the 3 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

19 April, 4 figure 5, the damping coefficient obtained by summing up the damping calculated from both the methods given the magnitude around.. At this calculated magnitude, it can summarize that the addition viscous damping by using Morison drags term can be helped to correct the damping coefficient and corrected the motion response estimated at the damping dominated region. Non-dimensional Damping Potential Damping Total Damping Viscous Damping Wavelength, m Figure 5: No dimensional Heave Damping for semi-submersible model 6. Morison Drag Force and Heave Force Besides smaller predicted heave damping, the heave force also under-predicted by diffraction potential theory. As mentioned in the earlier, the small predicted heave force is due to the cancelation of force due to the pressure distribution on the top side and bottom side of the pontoon. As shown in figure 6, the heave force predicted by the diffraction potential theory experience this force cancellation phenomenon at the wavelength around 7.5 meters. At this wavelength, it is obtained that the heave motion response calculated by this diffraction potential theory is dropped to nearly zero and give a non-rational result. As shown in figure 6, the heave force calculated by the diffraction potential theory will increase significantly from wavelength meter to wave length.6 meters and then follow by significant reductions by increasing of wavelength until where the calculated wave force become nearly zero at a wavelength around 7.5 meters for this selected semi-submersible structure. After the significant drop, the heave force calculated by this diffraction potential theory will increase gradually when wavelength increasing. For the drag force calculated by Morison drag term, it is obtained that the tendency of heave force is different compared to the heave force calculated by the diffraction potential theory. The heave force calculated by the Morison drag term is increasing rapidly from wavelength.5 meters to wave length 3.4 meters before it is reduced slowly to zero drag heave force by increase of wavelength. To combine the heave force contributed by both the methods, the summation of force is similar to the method of combining the initial force and drag force applied in Morison equation. In this study, the heave force calculated by the diffraction potential theory is assumed as the initial force term in the Morison equation. At the same time, the drag term for the total force is contributed by the linearly drag force from the drag term of the Morison equation. Both the heave force contributed by both the method is total up by vector summation theory. By referring to figure 6, it is obtained that the tendency of total heave force which total up by involved the diffraction force and drag force will no return to zero compared to the heave force calculated by diffraction potential methods. From the figure, it is observed that the total heave force will follow the diffraction force for the region of wave length other than 7.5 meters due to the diffraction force is significantly higher compared to the drag force. The role of the drag force in this calculation is to correct the heave force in the region where cancellation of force occurred in the diffraction potential theory. By the existing of the drag force from the Morison drag term, it is obtained that the drag force is shifted to the acceptable level and did not trend down to become zero where it is the main factor to causing the absolutely low heave motion response made by diffraction theory at the region. Nondimensional Heave Force Potential Force Drag Force Total Force Wavelength, m Figure 6: Heave force semi-submersible model 6.3 Heave Motion Response The heave RAO calculated by the diffraction potential theory and the corrected diffraction potential theory by the Morison drag term is presented in figure 7. The experimental data collected is only ranged from wavelength around meter to wavelength around 9 meters due to the limitation of the wave generating device in the laboratory. Comparison between the heave response calculated by the diffraction potential theory with and without Morison drag term correction is also presented in the figure 7. From the figure, it can be obtained that the diffraction potential theory with drag term correction is more accurate compared to the one without correction. The tendency of the heave response 4 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

20 April, 4 calculated by the diffraction potential theory with and without drag correction method shown non-similarity start from the wavelength around 3 meters. The calculated numerical result without the Morison drag correction is no agree with to the experimental result especially in the region where the wave frequency closed to the structure natural frequency (wave length equal to 9 meters). It can be observed that the drag force from the Morison equation is significantly important to estimate the heave motion response for semi-submersible structure in figure 7. By involving the drag effect for the calculation, the tendency of the numerical result will closer to the experimental result. Therefore, it can be summarized the neglected of the drag effect on the estimate heave response of semi-submersible like the diffraction potential theory will lead to wrong prediction of heave response in the region where the motion is dominated by damping. The reason for this observation are also explained in the figure 5 and 6 where it can obtain that the damping coefficient and heave force is under-predicted by the diffraction potential theory. Heave Response Experiment Diffraction and Morison Wavelength, m Figure 7: Heave motion responses for semi-submersible model 6. CONCLUSION Diffraction Theory In the conclusion, this paper was presented the correction method to improve the tendency of heave response calculated by the diffraction potential theory. In general, the diffraction potential theory is a good method to predict the motion of offshore structure especially semi-submersible in short time. Compare to the experimental result, it is obtained that the pure diffraction potential theory will wrong predicted the heave response in the region where the heave motion is dominated by damping or drag term. The weakness of the diffraction potential theory to neglect the drag effect was caused the damping and the heave force smaller than the actual situation and lead to wrong heave response tendency at the damping and drag dominate region. By involving the drag calculation using the drag term from Morison equation, the less accurate of damping and heave force calculated by diffraction potential theory can be corrected. In this paper, the numerical results calculated by the proposed method shown that the surge, pitch and heave motion response in head sea condition are agreed between the numerical result and experiment result. Therefore, it can be concluded that the diffraction potential theory with the Morison drag correction can be a suitable numerical approach to estimate the motion of offshore floating structure especially semi-submersible structured. ACKNOWLEDGEMENTS The authors would like to gratefully acknowledge to Marine Technology Center, UniversitiTeknologi Malaysia for supporting this research. REFERENCE. Hess, J. L., Smith, A. M. O., (964).Calculation of Nonlifting Potential Flow About Arbitrary 3D Bodies, Journal of Ship Research.. Van Oortmerssen, G., (979).Hydrodynamic interaction between two structures of floating in waves, Proc. of BOSS 79. Second International Conference on Behavior of Offshore Structures, London. 3. Loken, E.,(98). Hydrodynamic interaction between several floating bodies of arbitrary form in Waves, Proc. of International Symposium on Hydrodynamics in Ocean Engineering, NIT, Trondheim. 4. Wu, S.,Murray, J. J.,Virk, G. S.,(997). The motions and internal forces of a moored semi-submersible in regular waves, Ocean Engineering, 4(7), Yilmaz, A. Incecik,(996).Extreme motion response analysis of moored semi-submersibles, Ocean Engineering, 3(6) Söylemez, M.,(995). Motion tests of a twin-hulled semisubmersible, Ocean Engineering, (6) Clauss, G. F.,Schmittner, C.,Stutz, K., ().Time-Domain Investigation of a Semi Submersible in Rogue Waves, Proc. of the st International Conference on Offshore Mechanics and Arctic Engineering), Oslo, Norway. 8. Matos, V. L. F.,Simos, A. N.,Sphaier, S. H., (). Secondorder resonant heave, roll and pitch motions of a deep-draft semi-submersible:theoretical and Experimental Results, Ocean Engineering, 38(7 8) Wackers, J. et al., (). Free-Surface Viscous Flow Solution Methods for Ship Hydrodynamics, Archive of Computational Methods in Engineering, Vol Afrizal, E., Mufti, F.M., Siow, C.L., Jaswar, (3).Study of Fluid Flow Characteristic around Rounded-Shape FPSO Using RANS Method, The 8 th International Conference on Numerical Analysis in Engineering, pp: 46 56, Pekanbaru, Indonesia.. Jaswar et al, (). An integrated CFD simulation tool in naval architecture and offshore (NAO) engineering, The 4 th International Meeting of Advances in Thermofluids, Melaka, Malaysia, AIP Conf. Proc. 44,pp: Abyn, H., Maimun, A., Jaswar, Islam, M. R., Magee, Bodagi, A., B.,Pauzi, M., ().Model Test of Hydrodynamic Interactions of Floating Structures in Regular Waves,Proc. of 5 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

21 April, 4 the 6 th Asia-Pacific Workshop on Marine Hydrodynamics, pp: 73-78, Malaysia. 3. Abyn, H.,Maimun, A., Jaswar, Islam, M. R., Magee, A.,Bodagi, B., Pauzi, M., ().Effect of Mesh Number on Accuracy of Semi-Submersible Motion Prediction, Proc. of the 6 th Asia-Pacific Workshop on Marine Hydrodynamics, pp: , Malaysia. 4. Siow, C. L., Jaswar, Afrizal, E., Abyn, H., Maimun, A., Pauzi, M., (3).Comparative of Hydrodynamic Effect between Double Bodies to Single Body in Tank, The 8 th International Conference on Numerical Analysis in Engineering, pp: 64 73, Pekanbaru, Indonesia. 5. Tiau, K.U., Jaswar, Hassan Abyn and Siow, C.L., (). Study On Mobile Floating Harbor Concept, Proc. of the 6 th Asia-Pacific Workshop on Marine Hydrodynamics, pp: 4-8, Malaysia. 6. Cengel, Y. A, Cimbala, J. M. (). Fluid Mechanics Fundamentals and Application. nd Ed. 7. Kvittem, M. I.,Bachynski, E.E.,Moan, T., ().Effect of Hydrodynamic Modeling in Fully Coupled Simulations of a Semi-Submersible Wind Turbine, Energy Procedia, Siow, C. L., Abby Hassan, and Jaswar, (3). Semi- Submersible s Response Prediction by Diffraction Potential Method, The International Conference on Marine Safety and Environment, pp: - 8, Johor, Malaysia. 9. Siow, C. L., Jaswar, K, and Abby Hassan, (4). Semi- Submersible Heave Response Study Using Diffraction Potential Theory with Viscous Damping Correction. Journal of Ocean, Mechanical and Aerospace Science and Engineering, Vol. 5.. Nallayarasu, S. and Siva Prasad, P., ().Hydrodynamic Response of Spar and Semi-submersible Interlinked by a Rigid Yoke - Part : Regular Wave, Ship and Offshore Structures, 7(3).. Christina Sjöbris, ().Decommissioning of SPM buoy, Master of Science Thesis, Chalmers University of Technology, Gothenburg, Sweden.. Journee, J.M.J and Massie, W.W. (). Offshore Hydromechanics. ( st Edition.), Delf University of Technology. 6 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

22 April, 4 Energy Transmission to Long Waves Generated by Instantaneous Ground Motion on a Beach Arghya Bandyopadhyay, a,* and Avijit Mandal, b a) Department of Mathematics, Khalisani College, Chandannagar, Hooghly, India 7 38 b) Baidyapur Ramkrishna Vidyapith, Baidyapur, Burdwan, India 73 *Corresponding author: b.arghya@gmail.com Paper History Received: -March, 4 Received in revised form: -April-4 Accepted: 5-April-4 ABSTRACT Historically speaking, all high frequency earth-quakes do not produce tsunami which is evident from several earthquakes that took place in Indian Ocean between 4 and 6. The works of Geist et.al [ 6] and Ammon et.al [ 5] are good examples of such study through which they have pointed out the miserable failures of the existing warning system. The reasons of no-generation of tsunami due to large quakes may be several but in this article we have tried to throw some light on this puzzle and tried to analyze energy transmission to a tsunami motion at steady state and have shown that no energy transmits for certain frequencies of the forcing parameter. We discuss here tsunami waves which are generated by instantaneous bottom dislocation where the ocean floor is taken to be of variable slope and analytical solutions are provided correct to all time t. KEY WORDS: Tsunami Waves; Shallow Water Equations; Hankel Transform; Hankel Functions; Asymptotic Expansion. NOMENCLATURE η Wave elevation/surface displacement η st, u st surface displacement and velocity at steady state (J ν, Y ν ) Bessel function of first and second kind of order ν H(t) Heaviside unit function ( ) Hankel function H ν Sµ, ν (z) Lommel s function. INTRODUCTION Our interest is to study transmission of energy in the generation and propagation of long waves due to underground upheaval in an ocean with variable slope. The approach is an analytical one where we have restricted ourselves in solving forced long linear shallow water equations, the solution of which, it seems, is not found till date in variable ocean floor. For a beach of r variable slope y = qx, q >, r >, referred to horizontal and vertical directions as x-and y-axis respectively waves are generated by an instantaneous ground upheaval, along with a prescribed initial elevation and a velocity of the free surface at the instant before the ground begins to move. In conformity with Tuck and Hwang s analysis of long wave generation due to arbitrary ground motion over a uniformly sloping beach (r = ), we firstly show that it is possible to find a non-singular solution of the problem for all time t when the ocean slope varies. Then by taking a very general type of time dependent bottom dislocation we have been able to split the integrals in two parts one representing the waves due to free vibration which we claim to be the forerunners. It is shown that the forced waves (the second contributory part of the wave integral) will eventually catch up these forerunners and occupy the total wave spectrum beyond the half period of the forcing parameter. Assuming a time periodic ground motion, we next show that a steady-state exists. At this stage a noteworthy feature is observed of no transmission of energy from a finitely distributed time-periodic ground motion for a certain set of values of the disturbance function. This kind of paradoxical result was first observed by Stoker for steady-state surface waves in infinitely deep water (Stoker, J.J., 957). Introduction of 7 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

23 April, 4 small viscosity of the fluid may produce some amount of spreading of energy but that does not explain the huge non-transmission of energy which we found analytically over a large ocean area. Our attempt to find analytical solution of the problem helps us to understand the influence of variable bottom slope on wave elevation and velocity which might be helpful to understand the evolution of tsunami waves induced by near-shore earthquakes [Tinti and Tonini, 5]. Following the comments of Weahausen and Laitone (Surface waves, 96), and Pelinovsky () we assert that energy transmission explained here may also prove to be relevant in generation of long waves with variable pressure distributions. η = η x), η & = (x) on y = (4) ( η If η and η are small compared to h and u is small compared with the local wave speed gh (3), after using (), may be linearized to η η + (uh ) =, t x t (5) u η + g =. t x (6), equations () and Eliminating u(x, t) from (5), (6), and using suffix notation for partial differentiation, we obtain the partial differential equation satisfied by η: η η = η (7) tt gh (x) ηxx gh (x) x tt When h and η are given, it is required to determine η as the solution of (7) subject to the initial condition (4). The horizontal velocity u is then found from (5); for this purpose, we may impose a physically reasonable boundary condition at x =, namely η uh ~ h as x (8) x r When h (x) = qx, q >, r >, equation (7) suggests that we consider the solution of the ordinary differential equation Fig. : Schematic diagram of the sea-bottom motion and symbolic definitions.. PROBLEM AND ITS SOLUTION: We take the vertical upward direction as the y-axis, and the undisturbed horizontal surface of the sea as the xz -plane of which the axis Oz is along the shoreline. The sea is supposed to be bounded by a beach of variable slope given by the equation y = h (x) at equilibrium (Fig. ). We assume a two-dimensional motion in which long waves are excited by a sudden bottom upheaval of height η (x, t) accompanied by an initial surface displacement η (x) together with an initial vertical surface velocity η (x). If u(x, t) is the horizontal velocity, η(x, t) is the surface displacement and h h(x, t) = h (x) η (x, t) () is the depth at the point x, at time t >, the non-linear shallow water equations are ( η + h) + t x u u η + u + g = t x x At t = -, we have { u( η + h) } =, (). (3) r r ζ v ( ζ) + rζ v ( ζ) + β γ v( ζ) = (9) for the determination of η. For γ, the general solution of this equation is [Erdélyi et. al. HTF, 953] α γ α γ v ζ) = c ζ J ( βζ ) + c ζ Y ( βζ ), () ( ν where J ν ν ν and Y denote respectively Bessel functions of first and second kind of order ν, and r r r α =, γ =, ν = ± () r For γ =, that is r = the general solution of (9) is C v ( ζ) = + D, (C, D) = constants. () ζ Equations () and () show that v ( ζ) and v ( ζ) cannot be both finite at ζ = (in other words, η and u cannot be both finite at x = unless c, and γ. (3) To fix up the sign in ν in (), we consider the two cases: I. < r <. Then γ > and we have, as ζ +, α γ α+νγ r η ~ ζ J ( βζ ) ~ ζ = ζ or ζ, u ~ η ζ ν ~ ζ or ζ r 8 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

24 April, 4 according as the sign is + or in the expression for ν in (). Clearly η and u are both finite at ζ =. If we take the + sign in the expression for ν in (), that is if r ν =. r This is also consistent with the condition (8). II. r > Then γ <. As ζ + γ α ζ γ γ J ( βζ ν ζ r 4. Then ) ~ ζ γ η ~ ζ = as ζ +. Therefore the solution is not bounded at the origin when γ <, that is when r >. Consequently, we confine ourselves to the case < r < with the value of ν given r by ν = in the subsequent part of the article. r To solve the equation (7) subject to the given initial and boundary conditions, we assume that η η(x,t) = ξa( ξ,t) x ( r) J ( ξγ ν γ x ) dξ (4) Using this in (7), we obtain, by means of (9) and (), with c, the integral equation of first kind ( r) r η& (x,t) = (A&& + σ A) ξ x J ( ξγ x ) dξ (5) where σ = ξ(gq) (6) Then solution of η is obtained with the help of Hankel inversion theorem [Erdélyi et. al., Tables of Int. Trans., (954)] as η(x,t) = Where ( γ gq ) α ( r) x ν ( r) J ( ξγ ν ν J ( ξγ γ α )dα t γ x )dξ && ζ ( α,s)sin σ(t s)ds (7) ζ x,t) = η (x,t) + η (x, t)h(t) + t (x, t)h(t) (8) ( η where H is the Heaviside unit function. We note that for r = this expression reduces to that of η found for constant slope beach. [Tuck and Hwang, 97]. To evaluate the above integral we take η x, t) = η (x, t) and ζ ( x, t) = η (x, t) = ζ(x)t(t) where i T(t) = H(t τ) + ( e ωt )H( τ t) ( =, ω = π / τ, (9) we have been able to evaluate the above integral for all time t. In the above the t-integral reduces to m t ( ) ( ) m+ i dt t j m m ( t) + m= m! σ + ω ω ω σ fo + ω r t < τ where ( z) π z J (z) jm m+ =, with the help of a very nice result [Erdélyi et. al. HTF, 953, pp.58] m= m m ( θ t ) θ J ( θ) π m (cos t cos θ) =. m! Then we spilt the ξ-integral in two parts one from ξ = to ξ =ω/ (gq) [the first part], and can be evaluated by another result which combines product of two Hankel functions as an integral of a single [Erdélyi et. al., Tables of Int. Trans., 954, Vol II, pp. 9] J ν γ γ γ ν γ ( ξγ α ) J ( ξγ x ) = π ( 4γ α x ) ( λξ) J ( λξ)( cos θ) n= ν ξ x 4γ γ α F n, ν n; ν + ; x γ π π n! Γ(n + m + ν + ) ζ ( α) dα ν γ dθ This spilt corresponds to η, say, of η and corresponds to the free vibration and can be treated as the forerunners. These waves in this spectrum dominate for first few minutes, to be precise for the half period of the quake forcing. ν+ + ( ) ν t m ξ ωt η = (γ) + iω dt j ω Γ ν + m ( t) ( ) ( m + ) m= n () On the other hand, the second part of ξ-integral from ξ=ξ to contribute η, say, of η representing the forced wave part and they catch up the free waves beyond half period τ and dominate the wave spectrum gradually for t > τ.. Discussion on the Nature of Waves with the Help of Some Illustrative Figures. Before we proceed further and discuss the steady-state nature of the waves and the energy transmission let us provide some illustrative figures showing the nature of η and η in an attempt to distinguish them foe small time η t H< tl η η Fig. : Depicting η & η for small time when r =.7. 9 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

25 April, 4 The above figure shows the prominence η over η for small time when the value of r =.7 The next graph (Fig.) illustrate nature of η for the same value of r =.7 and indicates that there might be some sort singularity at t = τ which needs further analytical investigation for the motion t > τ for a definite conclusion. 4 3 h which we have already mentioned that η increasing indefinitely indicates as t increasing is probably due to the sudden disappearance of the bottom vibration at t = τ. In this article although we are interested to discuss the energy transmission at steady-state but it is perhaps not out of context to say few words about η, at least qualitatively. The spilt of η namely η which comes from the second part of ξ-integral in (7) while integrating it from ξ=ξ to consists of three parts: one of which has a wave form and the other two are standing disturbances, analytical expressions of which is valid for /3 < r < 4/3. We restraint ourselves of writing those complicated expressions rather give some illustration of η below for different sloppiness of ocean floor Fig. 3 Depicting η for small time when r =.7. t<t h We will provide another illustration for another value of r just to show the equivalence of the results for different values of r and the prominence of η over η in small time: t<t η t H< tl η η Fig. 4: Depicting η and η for small time when r = h Fig, 5: Depicting η for small time when r =.8. t<t In the above cases while depicting the results which well established analytically we have taken the half period of the quake forcing that is τ = seconds and use have been made of the software Mathematica 5.. An interesting feature of that comes out of these figure Fig. 6. The graph of η when t < τ and for r = h t<t Fig. 7: The graph of η when t < τ and for r =.8. The figures (7 ) - (8) indicate the dominance of η in the wave spectrum that is going to happen after some time, η actually corresponds to the forced wave part of η which will certainly govern the spectrum over those waves which are small and corresponds to the natural frequencies of wave motion.. Periodic Ground Motion: Steady-State Solution Of η and u We assume η (x), η (x) ; η (x) = f (x)exp(iωt), t > and show that a steady state ( t ) exists and also determine the corresponding values of ηand u. Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

26 April, 4.3 Steady-State Values Of η When the integration with respect to s in (7) is completed, we get ( r) η = ( ω γ)( gq) x + iω t where F( σ) = f ( ξ) = () ( σ - ω) ( ωsin σt σsin ωt)f( σ)dσ ( gq) γ ( σ + ω) J ( ξγ x )f ( ξ) α ( r) J ( ξγ ν ν γ, () α ) f( α) dα. (3) We spilt the σ -range in () into the sub-intervals [, ω ] and [ ω, ). By the help of known results on Fourier integrals, the part of the integral in () over the interval [, ω ] is asymptotically equal to O(t ) sin ωt ω ( σ ω) σf( σ)dσ ( as t. (4) The remaining part of the integral in () is written as η = ωcos ωt ω - sin ωt ( σ - ω) ω F( σ)sin( σ ω)tdσ ( σ - ω) { σ ωcos( σ ω)t} F( σ)dσ (5) Combining (4) and (5), we get for the integral in () the expression O(t ) sin ωt (p.v.) + ωcos ωt ω ( σ - ω) + ωsin ωt (p.v.) ω ( σ ω) ( σ - ω) σf( σ)dσ + F( σ)sin( σ ω)tdσ + F( σ) cos( σ ω)tdσ as t (6) Here the symbol ( p.v.) indicates the Cauchy Principal value of the integral in question. Following Bochner [ Wehausen, J.V. and Laitone, E.V. Surface waves. Handbuch der Physik IX (Springer, Berlin, 96)], the asymptotic values of the third and fourth terms of (6) are respectively ω cosωt[ π F( ω) + O(t )] and O(t ) ωsin ωt, as t (7) The results in (7) hold provided (i) F( σ) is differentiable with respect to σ in [, ) (ii) F ( ω) exists, (iii) F( σ ) and F ( σ) are each absolutely integrable in [ ω, ). Equation () then gives ( r) st = ( πω γgq) x exp{ i ( π +ωt )} f( ω/ () γ γ [ Hν ( ωx γ gq) ( iν π) S, ν( ωx γ gq) ] ( r) ( ω γgq) x exp(iωt) ξ( ξ p ) {f( η gq) ν γ ξ) f(p)} J ( ξγ x )dξ for < r < 5 3 (8) h u st = ωγ x πω exp(iωt) - ipν( ν + )f (p)s ( ) ( ) γ gq f (p)h ν+ ( pγ x ) γ ( pγ x ) +, ν+ γ + i ξ ( ξ p ) {f ( ξ) f (p)} J ν+ ( ξγ x )dξ for < r < 5 3 (9) Here Y ν denotes Bessel function of the second kind, and S is Lommel s function. ν, µ The first term of both η st and u st, as given below, represent progressive waves: ( r) η = πω γgq f ( ω/ gq)x () exp{ i ( π + ωt) } H ( ωx γ ν γ gq ) (3) h * = πω γ u gq x x exp(iωt)f (p)h ( ) γ ( pγ x ) ν+ We also note that η * is an integral of the hyperbolic equation r η * + rx x r η * = x η * ( gq ) t (3) The rest part of η st as well as u st represent clearly standing waves. Since γ > in our case, we may use the asymptotic expansion of H ( ) γ (z) for z to obtain η * for large x: η ~ ( π γ) ( ) ( ) ω gq 3 r 4 f ω gq x 3π γ exp i ωt + ( ωx γ gq ) + νπ 4 (33) The wave described by (33) propagates towards x + according to the equation x = γ gq t (34) ( ) γ Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

27 April, 4 Thus this wave moves with a variable acceleration unless r = when the acceleration is constant [ cp. Tuck & Hwang, 97, pp - 449]. The height of the wave decreases with the time or r 4 x distance from the source, according to the factor (which r (4 r) is equivalent to t ). Since the depth increases as x, this corresponds to Green s law of shallow water waves..4 Transmission of Energy A notable feature of the steady-state solution is that no energy is transmitted through the liquid for frequencies ω = ω which make f ( ω gq ) =, and hence η * =, u * =, the part ηst η * and u st u * being a standing wave. These critical frequencies may form a countable infinite set as it is shown by the following example: η (x,t) = Pexp(iωt), < x < a, t > = x > a with h (x) = qx (36) Then f ( ξ) = Pa a 5 4 α 4 J / 3 4 a ξα 3 4 dα = n (35) ( / a 4 Pa ξ) J ξa 3 / 3 3 (37) The zeros of J ν (x), for ν > and x real, are known to be countably infinite. If γ 3, n be the n-th position zero of J 3 (x) =, the critical frequencies ω n are given by ω ( ) n = a gq γ 3, n, n =,, (38) 4 if we apply the sea bed deformation due to earthquake as given by Okada s solution [99] we may perhaps need to employ some numerical work although in that case one has to remain cautious about oscillatory nature of the wave integrals under consideration. The main purpose of this work is to provide an analytical solution for the waves and discuss qualitatively about those waves for the case when instantaneous motion occurs at sea-bed with variable bathymetry and the energy transmission at the steady state. The place of this bottom dislocation is perfectly arbitrary and is not scaled from the shoreline. This situation is somewhat close to the real tsunami generation mechanism particularly when the nonuniform nature of the slope of ocean comes into play. The effect of the non-uniform nature of the bottom slope is quite visible with the steady-state analysis of the farfield waves. One of the central challenges in tsunami science is to rapidly access a local tsunami severity from the first rough earthquake estimations. In the current state of knowledge, false alarm is perhaps unavoidable (Dutykh et.al. ), but the study we proposed here may be taken as a first step to that direction as we have addressed the all important issue of energy transmission to tsunami waves though it is in the steady-state. ACKNOWLEDGEMENTS Authors are deeply indebted to Prof. (Retd.) Asim Ranjan Sen, Department of Mathematics, Jadavpur University, Calcutta, India for his help and suggestion during the preparation of this paper. REFERENCE 3. CONCLUSIONS This study tries to reach out to the big anomaly between the tsunami heights with the so-called early predictions through the energy budget estimation although we know our solution is somewhat crippled as we have restricted ourselves to a linear model. Having said so, we wish to point out that for the study of tsunami wave motion certain important parameters like wave-evolution, the shoaling and wave run-up are well approximated by linear theory, and that too with high degree of precision (Edward Bryant, 3, Synalokais, CE., 99). Needless to mention that bathymetric obstacles in large ocean, creating variability of ocean floor starting from continental slope to shoreline plays an important role affecting tsunami translation and the energy transmission not only with teleseismic tsunami but even with tsunamis generated by near-shore earth-quake (Tinti & Tonini, 5). Leaving aside the actual physical dislocation of the sea floor the solution provided here is correct for all t. In fact. Geist et. al. (6), Differences in Tsunami generation between the December 6, and March 8, 5 Sumatra Earthquakes. Earth Planets Space 58, 6, Ammon C. J. et. al. (5), The 7 July 6 Java Tsunami Earthquake, Geo. Phy. Let. 33, L Stoker, J.J (957). Water Waves, Interscience Pulishers, New York. 4. Tinti, S. and Tonini, R. (5), Evolution of tsunamis induced by near-shore earthquakes on a constant slope ocean, J. Fluid Mech. Vol 535, Weahausen, J. V. and Laitone, E. V. (96), Surface waves, Handbuch der In Physik, Vol. 9, Part. 3, Springer Berlin, Tuck, EO and Hwang, LS (97)., Long wave generation on a sloping beach, J. Fluid Mech. Vol 5, pp Pelinovsky,E and Talipova, T. et. al.(), Nonlinear mechanism of tsunami wave generation by atmospheric disturbances, Natural Hazards and Earth Sys. Sc. Vol, Erdléyi et. al. (954), Tables of Integral Transforms, Vol II, pp 9, McGraw-Hill. 9. Erdléyi et. al. (953), Higher Transcendental Functions, Vol II, pp 58, McGraw-Hill. Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

28 April, 4.. Liu, PL-F, Lynett, P and Synolakis, CE (3), Analytical solution for forced long waves on a sloping beach, J. Fluid Mech. Vol 478, 9. Oberhettinger, F (97), Tables of Bessel Transforms, Springer. Edward Bryant (3), Tsunami the underrated hazards: CUP 3. Synolakis, CE. (99), Tsunami Runup on Steep Slopes: How Good Linear Theory Is, Natural Hazards, Vol 4, - 34, Kluwer Academic Publishers. 4. Okada, Y. (99), Internal deformation due to shear and tensile faults in a half-space, Bull. Seism. Soc. Am., Vol 8, pp Dutykh, et. al. (), On the contribution of the horizontal sea-bed displacements into the tsunami generation process, Ocean Modelling, 56, Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

29 April, 4 Study on Wave Buoy Legged Spider Power Device Priyanto, A, a,*, Maimun, A, b, Zamani, M, a, Jaswar Koto, a,c and Kader, A.S.A, b a) Department of Aeronautical, Automotive & Ocean Engineering, Universiti Teknologi Malaysia b) Marine Technology Center, Universiti Teknologi Malaysia c) Ocean and Aerospace Research Institute, Indonesia *Corresponding author: agoes@fkm.utm.my Paper History Received: 7-December-3 Received in revised form: 5-April-4 Accepted: 8-April-4 ABSTRACT This paper studied on Wave Buoy Legged Spider power device, a floating wave energy system based on linear generator. The device contains horizontal cylinders arranged such that it looks like the legs of a spider. Inside cylinders will be equipped with a linear generator. During wave motions, some rotors of the linear generators slide forward and backward, thus generating electricity. As a case, a conceptual design of the Wave Buoy Legged Spider device using floating balls of Malaysian wave buoy for an ocean site in Terengganu, West Malaysia is presented. The wave energy was approximately assessed based on observed wave data. Furthermore a method to determine the directional wave spectra by using nonlinear programming has been proposed with introducing a correction factor in order to avoid the concentration of power spectral density. The capability of this method has been verified by the analysis with the data of the experiments of the floating ball response. KEY WORDS: Conceptual design; Wave Buoy; Wave Power; Directional; Energy; Device.. INTRODUCTION This paper presents an efficiently wave buoy legged spider of wave power device that used the floating balls [] from Malaysian wave buoy. As we know that a wave power device will convert the energy of wave motion into the high-speed rotation of generator. The process can be divided into three steps, i.e., collecting wave energy, transmitting energy and generating electricity by generator []. The procedures usually make a wave power device complicated, and increase energy loss, hence lowering the energy efficiency of the device, such as Archimedes Wave Swing [3] and Wave Dragon [4] may need high construction cost, but not for the new wave power device, called wave buoy legged spider. This power device utilizes linear generators and thus is able to simplify energy transmission and decreases energy loss during conversion. The device is also constructed by simple structure and low cost, and will show high energy efficiency in the case study section.. WAVE BUOY LEGGED SPIDER As showed in Fig., the Wave buoy legged Spider device is a floating system incorporating eight horizontal cylindrical members, called power antennas. The antennas look like the leg of a spider. The major components of the device include power antennas, floating balls, an energy conservation control center (or control center), a buoyant plate, submarine electrical cables, mooring lines, connecting bars, and elastic ropes. The power antennas are rigidly connected to the buoyant plate through connecting bars. Four floating balls that used Malaysian wave buoys are attached on each power antenna. Inner floating balls may be connected together through flexible elastic ropes so as to integrate the power antennas. Buoys are also attached at the ends of each power antenna to provide additional buoyancy. The control center incorporates an energy storage box and a series of components used for power storage and transmission, such as transformer and rectifier. The energy storage box could be a kind of typical small battery system as described in [5], which is able to conserve a small portion of electricity generated by the power antennas. The stored power is used for the device s own maintenance, and the majority of the generated electricity will be 4 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

30 April, 4 transmitted to the shore via submarine electrical cables. The floating balls enable the power antennas to absorb surface wave energy to the greatest degree when the device is fluctuating with wave. In addition, adaptive variable damping may be employed to enhance the efficiency of the Water Spider device. Adaptive variable damping can be used to achieve the best damping given random waves ([6]; [7]). The Wave buoy legged Spider device is anchored at seabed by mooring lines. Power antenna Floating ball Control center exchange between the kinetic energy and the potential energy of the rotor, thus helping the sliding of the rotor in the chamber. If the air in the chamber is expelled, the energy loss may be further reduced because of decreased air resistance. Given wave motions, the rotor in the linear generator slides forward and backward, leading to the change of magnetic flux in the metal coils. As a result, the induced electromotive force converts wave energy into electrical energy. The power generated by the linear generator is transmitted to the control center via the connecting bars attached at one end of the power antenna.. Floating ball The floating ball is a Malaysian wave buoy as shown in Fig.3 which follows the movements of the water surface, and monitors waves by measuring the vertical acceleration of the buoy. The discrepancy between vertical movements of the wave buoy and the movement of the sea surface is small. When an attached wave buoy follows the waves, the force of the flexible elastic ropes will change. This force is produced by changing immersion of the buoy, resulting in an error of maximum.5%. With decreasing wave length, the buoy motion will deviate from the wave motion if the wave length is less than 4 m (wave period below.6 sec). If the wave length is less than.5 m (wave period.5 sec) the response of the buoy decreases fast with increasing wave frequency. Figure : Wave Buoy Legged Spider. Power antenna As the component of the Wave buoy Spider device, the power antennas convert wave energy into electricity. The power antennas adopt the wave power capsule technology developed by Zhang et al. (). The capsule technology uses linear generators, which generate electricity by the sliding of their rotors (Zhang et al., ). As shown in Fig., a power antenna accommodates a sliding rotor, a stator, and insulating rubber materials. The stator is mainly composed of metal coils, insulating barrier, and insulating rubber layers. The outside of the metal coils is coated with insulating paint. Figure 3: Floating ball (unit in mm) Figure : Power antenna capsule The rotor consists of permanent magnet with strong magnetic field, wheels, and springs ([8]; [9]). The wheels reduce the friction between the rotor and the sliding chamber. The spring can buffer the collision between the rotor and the end wall of the sliding chamber. The deformation of the spring results in the Wave data which was measured by the accelerometers inside the floating ball are collected to provide essential information for the design, construction and performance monitoring of wave buoy legged spider power device... Accelerometer For an accelerometer to accurately sense and generate useful data, it must be properly coupled to the test object. This requires that the accelerometer mounting be rigid over the frequency range of interest. The methods for mounting an accelerometer usually 5 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

31 April, 4 depend on the accelerometerr and the text structure. In order to obtain vertical displacement, the acceleration signal is integrated twice. The integration process limits the response of the wave rider buoy at low frequency to prevent slow changes in the accelerometer output and electronics to appear on the wave record.. Wireless System The wireless system block diagram is as shown in Fig. 4. The analog data from the accelerometer are converted to digital data; it will be sent to transmitter. Transmitter will than transmit the digital data to through antenna to receiver. When the antenna receiver receives the data by the omni-directional antenna, it will amplify the data before sending to receiver. After the data pass through the receiver, it will than pass through the SOC will then be sent to computer by USB. At the computer, the data will be displayed, and processed. to be 678 J/m, and the corresponding power (Pk) to be.96 kw/m. The total wave power (Pw), whichh incorporates both kinetic and potential energies, is thus estimated to be 5.9 kw/m. Figure 5: Site measurement POE Power SOC Digital Data (WPAN) SOC Power POE Power Power Supply Board On Boat/onshore Digital Data (TCP/IP) Laptop or PC Digital Data (TCP/IP) ECOV Digital Data (serial) ADC Board Analog Data Power Power Power Supply Board Power Accelerometer On Buoy Figure 6: Data measurement Figure 4: Wireless system For equipment installation at the wave buoy, the preparations on telemetry system are wireless devices (e-cov converters, gyro meter, Inline Power Injector POE, Wireless Outdoor Client Bridge / AP), power supply circuit and V rechargeable battery. The 4 rechargeable batteries were installed at the middle part of the buoy and reacted as ballast for the wave buoy while the wireless devices were installed at the inner platform. 3. SITE CONDITION The power potential of the Wave buoy legged Spider device for an ocean site in Terengganu, West Malaysia is approximately assessed as a conceptual application of the device. The floating ball has provided a typical observed wave record at the site, as showed in Figs.5 7. The average water depth is 9 m. The significant wave height (H/3) is.64m, and the corresponding wave period is 5.s. The average wave height is.45 m. It is assumed that the linear wave theory is applicable for the site. Conservatively, this case study considers H/3 and the corresponding wave period as typical wave characteristics for energy evaluation. Therefore the kinetic energy (Ek) is estimated Spectral Ordinate (m.s/rad) Malaysian Wave Buoy Pierson-Moskow itz JONSWAP Bretschneider Wave Frequency (rad/sec) Figure 7: Wave spectrum data measurement 4. CONCEPTUAL DESIGN The parameters of linear generator in other studies with similar wave climate are applied in this study for demonstrative purposes. Wu et.al [] and Danielssonn et al. [9] and Danielsson [] conducted a linear generator study based on regular wave, in 6 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

32 April, 4 which wave height and wave period were.5m and 4.5s, respectively. The wave characteristics are close to the significant wave height and corresponding wave period in this study, so the basic parameters of linear generator applied in Danielsson et.al [9] and Danielsson [] are used herein, showed in Table. A Wave buoy legged Spider device is hence conceptually designed, and Fig. 8 illustrates basic dimensions of the power antenna. An octagonal buoyant plate (side length.6 m) is adopted, and the diameter of the entire device is about 7.85 m. Considering the diameter of the device, the total output power for a unit width is.96 kw/m. In this case study, the total output power P * is estimated to be 5.7 kw. where λ (=β) is the angle between the power antenna and wave direction (see Fig. ) When a floating ball buoy is facing in following seas, there is a range of the encounter frequency of the wave buoy, which cannot be related to the wave frequency by a single-value transformation. The method to overcome this difficulty has not been well established, although studies to evaluate the one-dimensional wave spectra as well as the directional wave spectra have been extensively carried out in recent years. To determine the directional wave spectrum by using a nonlinear programming, the ordinates of wave spectrum at an arbitrary wave frequency are used as design variables and the optimization by using a nonlinear programming is carried out in the range of encounter frequency of the buoy. Fig. 8. Power antenna dimension Tabel. Parameter of Linear Generator Parameter Value Apparent power (kw) Voltage (V) Current (A) 9 Resistive (Ώ) 4 Width of stator (mm) 46 Length of stator (mm) 64 Width of magnet (mm) 55 Hysteresis Loss (kw).5 Eddy current loss (kw).7 Resistance loss (kw).75 To evaluate the utilization rate of wave energy for the conceptual design, an energy efficiency of the small-scale floating wave device, such as Wave buoy legged Spider, however, the potential energy may not be effectively utilized in practice. Hence an energy efficiency of the device is defined. P * η = () P k η is estimated to be 65.%. It can be observed that considering the effectively usable energy P k, the energy efficiency of the wave buoy legged spider device is relatively high. 5. Directional Wave Spectrum Due to the directionality of waves, the power antennas of a Wave buoy legged Spider device may not reach the full capacity P k, simultaneously. The effective output of a power antenna depends on a measured wave direction. The effective output (P e ) can be approximately estimated as follows: P e = P k cos λ () 5. Optimization Procedure In this section, we propose to determine the wave spectrum by using nonlinear programming [], in which the ordinates of wave spectrum at an arbitrary wave frequency are specified as design variables and the optimization has been carried out in the encounter frequency of the ship. The procedures adopted in this paper are as follows. ) Define the design variables which are the ordinates of the wave spectrum in the wave frequency ; S w ( ω) ) Estimate the spectrum of the buoy response, S ( ω) S x using the following relationship, π ( ω) = S w ( ω) x [ Ax ( ω, χ + χ c )] D( ω, χ c ) dχ c π x, by (3) Where: the directional function D ( ω, χ ) is assumed to be 4 cos χ. 3) Transform the estimated spectrum of the buoy response in the wave frequency S x ( ω) to the one in the frequency of S ω, encounter ( ) x e 4) Define the objective function F, ω ~ { ( ) ( )} F = ec S x ω e S x ωe (4) ω = ~ S x ( ω ) and ( ) e e S ω are respectively the estimated and x e measured spectrum of the buoy response in the frequency of encounter. 5) Minimize F under the following constraints, ~ S x ( ω ) dω = S x ( ωe ) dωe (5) 7 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

33 April, 4 5. Transformation Spectrum The spectrum of ship response in the frequency of encounter can be converted to the one in the wave frequency. However, there is the situation as shown in Fig. 9, in which one frequency of encounter is related to three values of wave frequencies. This is the reason why the transformation of the spectrum is difficult. ωe (rad/sec) S( ω) ΔS( ωe) I II III IV ΔS I ( ω) ΔS II ( ω) ΔS III ( ω) pitch in regular following waves. In the figure, the solid line shows the result of strip theory and the mark corresponds to the measured values, they have the same trends theoretically and experimentally. Z a/ ζ a. Heave Cal. Mea ω (rad/sec) θa/k ζ a. Pitch Cal. Mea ω (rad/sec) S( ω ) e ω (rad/sec) Fig. Heave and pitch responses in regular wave Figure 9: Transformation of spectrum from ωe ω ec ) ωe and ω ec (for Fig. gives the measured spectra of heave and pitch in irregular waves. cm sec. Spectrum of Heave deg sec. Spectrum of Pitch When a spectrum of buoy response in the encounter frequency is transformed from the one in the wave frequency, the power spectral density concentrates only in the region ωe ωec. However, the measured spectrum of the buoy response in the encounter frequency has a power spectral density even in the regionω e > ωec, and no concentrated power spectral density is appeared. Therefore, in order to deal with the concentration of the transformed spectrum in the region ω e > ωec, the correction factor has been introduced. S( ω e ) Comparison between measured and transformed spectrum Measured Et B Transformed Em A = Et A ω ec Em B Figure : Transformation of spectrum from ωe and ω ec (for ωe ω ec ) using correction factor. ω (rad/sec) e 5.3 Estimated Wave Spectra 5.3. Experiments in Towing Tank The experiments were performed in the towing tank of Universiti Teknologi Malaysia. The dimensions of the tank are.m (length) by 4.m (breadth) by.5m (depth). The buoy was freely drifted by towing under a carriage. Fig. shows the non dimensionalized amplitudes of heave and ω e (rad/sec) ω e (rad/sec) Figure : Measured spectra heave and pitch 5.3. Comparisons of wave spectra Fig. 3 shows the comparison between the estimated and measured wave spectra. In Fig. 4, the spectra of heave and pitch response between the estimated and measured in the encounter frequency with correction are compared Figure 3: Comparison between estimated and measured wave spectrum.5 cm sec. Wave spectrum Measured Design points ω(rad/sec) 8 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

34 April, 4 cm sec. Wave spectrum.5..5 Measured Design points ω(rad/sec) Figure 4: Comparison between estimated and measured wave spectrum with correction. 6 CONCLUSION The conclusions have been drawn as following items;. The small-scale wave device, the Wave buoy legged Spider concept is characterized by simple structure buoys, high energy efficiency, and convenient installation and maintenance. The device may provide a promising way for small-scale wave energy development.. For designing the Wave buoy legged Spider, a method to determine the directional wave spectra by using nonlinear programming has been used and the transformation of the spectrum has introduced a correction factor in order to avoid the concentration of power spectral density. The capability of this method has been confirmed by the analysis with the data of the experiments. 6. Polinder, H, and Scuotto, M, (5), Wave Converters and Their Impact on Power Systems. Future Power Systems, The Proceedings of International Conference on Digital Object Identifier. pp Fan, HY, (5), The Research of a New Floating Type Wave Power Device, Master's Degree Thesis, Tsinghua University. 8. Zhang, ZW, and Lou, DB, (), Study and Application of Wave Power Generation Capsule Technology, Patent 736, Danielsson, O, Thorburn, K, Eriksson, M, and Leijon, M,(3), Permanent Magnet Fixation Concepts for Linear Generator, Proceedings of the Fifth European Wave Energy Conference. pp -7.. Danielsson, O, (3), Design of a Linear Generator for Wave Energy Plant. Master s Degree Thesis, Uppsala Universitet.. Saito, K., Maeda, K, (997),.: An Estimation of Ocean Wave Characteristics Based on Measured Ship Motions -- Application of Nonlinear Programming to the Evaluation of Wave Spectrum --, Journal of the Society of Naval Architects of Japan, Vol.8, pp.3-37, (in Japanese).. Jaswar, C. L. Siow, A. Maimun, C. Guedes Soares, (3), Estimation of Electrical-Wave Power in Merang Shore, Terengganu, Malaysia, Jurnal Teknologi, Vol.66., pp.9-4. ACKNOWLEDGEMENTS The authors wish to acknowledge Universiti Teknologi Malaysia and Ministry of Higher Education of Malaysia (MOHE) for the research Vot.No.Q.J3.74.H REFERENCE. Wu, L, He, DS, Gou, W, and Zhou, SL (). Water Spider Wave Power Device: Conceptual Study. International Offshore and Polar Conference. pp Li, F, Ye, JW, and Gou, YF (6). Study of Wave Energy Generator System. Guangdong Shipbuilding. No 4, pp Czech, B, Bauer, P, and Polinder, H (9). Modeling and simulating an Archimedes Wave Swing park in steady state conditions. Power Electronics and Applications, EPE '9. 3th European Conference. pp Tedd, J, and Kofoed, JP (9). Measurements of overtopping flow time series on the Wave Dragon, wave energy converter. Renewable Energy. Vol 34, No 3, pp Green, J, Bowen, A, Fingersh, LJ, and Wan, YH (7). Electrical Collection and Transmission Systems for Offshore Wind Power, Offshore Technology Conference. pp Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

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