Dynamic Responses of Pontoons Connecting Process of Mobile Offshore Base

China 0cean Engnering，Vol.24, No.1, pp. 191- 198 .C 2010 Chinese Ocean Engineering Society, ISSN 0890-5487Dynamic Responses of Pontoons Connecting Process of Mobile Ofshore BaseTAN Zhen-dong (谭振东)*,1, ZHANG Yu (张宇)， WANG Guang-dong (王广东)",ZHANG Xing (张兴)* and SHAO Xiang-jun (邵相军)*a Military Transportation Institute of the General Logistics Department ，Tianjin 300161, Chinab TEDA Onhing Hi-Tech Co. LTd, Tianjin 300161 , China(Received 26 March 2009; received revised form 19 June 2009; accepted 29 September 2009)ABSTRACTThe dynamic responses of two pontoons while connected with each other in inregular waves are calculated by meansof three -dimensional (3-D) potential flow theory. The computation is to find the optimal status for connection at a certainsea state. On the basis of the relative motion of two pontoons in iregular waves, Visual FORTRAN programming lan-guage, as well as OpenGL (Open Graphics Library), is used to develop a set of virtual reality system of the relative mo-tion of two pontoons, which is fully interactive with realistic effect. 'The transfinite interpolation scheme is applied for themesh generation of wave surface, and the wave motion is simulated by surface elevation and calculated by 3-D potentialflow theory.Key words: pontoons connection; dynamic response ; 3-D potential flow theory; irregular uoues; simulation ; OpenGL1. IntroductionWith the coming of marine economy，ocean resources development has induced a batch of new in-dustries, such as offshore oil and gas, marine biotechnology ，marine chemistry and deep-sea mining.At the present time, the study on large floating structures becomes a hot issue and mobile offshore baseemerges with the times requirement .Within this field, many researchers (Dai, 2003; Wu et al.，1993; Kim and Chen, 1999; Yan,2005) studied the global response of mobile ofshore base, ignoring the analysis of the connecting pro-cess of the modules, which are elements of the base. Furthermore, some experiments have been per-formed to obtain the motion characteristics of the mobile offshore base. Yu et al. (2003), Riggs andErtekin (Riggs and Ertekin, 1993; Ertekin et al., 1993) calculated the connector load and analyzedthe dynamic characteristics of connectors.Until now, only a few researches have involved the coupled dynamics of two floating bodies, es-pecially pontoons connection as parts of the mobile offshore base. Xie and Gao ( 1999) used the linearthree- dimensional potential theory to calculate the hydrodynamic interaction between two bodies floatingin waves without restoring characteristics of ha-2003)， Chen and Fang中国煤化工( 2001), and Fang and Kim ( 1986) examined th:TYHCNMHGs travelling in close prox-* This work was financially supported by the National Natural Science Foundation of China (Grant No. 50579047)1Corresponding author. E mail: tzdpla@ 126. com192TAN Zhen-dong et al ./ China Ocean Engnering, 24(1), 2010, 191- 198imity at moderate forward speed during underway replenishment. Li (2001 ) developed an algorithm to .solve the free-surface Green function of zero forward speed in water of finite depth and in shallow wa-ter, and then numerically predicted the shallow water effect on two ship interactions in waves .In the present study, in consideration of the restoring characteristic of hawsers and reaction be-tween two floating bodies, the three-dimensional potential flow theory is adopted to predict the coupledmotion between two pontoons in irregular waves，which provides an accurate basis for the pontoon as-sembly operations. In addition, Visual FORTRAN programming language and OpenGL ( Open GraphicsLibrary) are used to simulate the relative motion of two pontoons in waves . The simulation program hasfriendly interface and distinct graphics.2. Pontoons Connecting MethodMobile offshore base is mainly composed of pontoons，including standard module, ramp module,T-module and so on. The basic unit consists of several modules with rigid connections. These units to-gether may form various kinds of floating structures or special elements. Every kind of module in thesystem has interchangeability and modular assembly can be implemented.Before pontoons being connected at sea, transport ship with modules, two tugs and other auxiliaryequipment should be positioned at the designated operating water areas. Modules are connected by thetug with the power unit services. The connecting process is shown in Fig. 1. Mooring cable is tied tothe corner of module which will be connected in water and the other end of the cable is tied to the tug.The crane is used to complete the launching operations. The connecting process is as follows: Moduleconnecting operations can be caried out at the third sea state. Pontoon module 1 and the tug are fixedthrough the cable. Rubber fenders are adopted to prevent the collision between hulls. Pontoon module2 and power unit are fixed through the cable, too. The two pontoon modules are closed up each otherby the operation of power unit， and make the two connector approximate alignment by eyeballing.Tractive rope, which passes through the hydraulic winch of pontoon module 1, links the slider connec-tor of pontoon module 2. Repeating the operation, we can layout the other one. Start hydraulic winch,narrow the gap between the two pontoon modules until the slider connector of pontoon module 2 gets in-to the corresponding slider connection box of pontoon module 1 and simultaneously butterfly connector' sarm get into the butterfly-wings-type box. Use the pin to fix the butterfly connector and brake shoe tofix the slider connector. Revoke tractive rope finally.3. The Coupled Motion Resp中国煤化工'WavesThere is a certain space between two pontoqTYHCN MH G,and therefore the exis-tence of multi- rigid-body interaction is inevitable. Wave loads on each module are different from thaton single rigid-body, and the motion can also be afected. As hydrodynamic interaction of adjacentpontoons, motion characteristics of each pontoon in waves are different from that with only a singlepontoon.TAN Zhen-dong et al . / China 0Ocean Engineering ，24(1), 2010, 191- 198AnchorUnit2UnitPower unitFig.1. Procedure of connecting pontoons.The 3-D potential flow theory is applied in the calculation of motion response between two floatingbodies in the iregular wave, where the effect of their interaction is considered. The stochastic processof iregular wave can be achieved by superposing a group of regular waves in different amplitude, fre-quency and relatively independent phase ( Wang，1993). The origin of the global coordinate systemOXYZ is located at the water surface between two floating-body systems, positive from sterm to bow inthe X-axis direction, positive to port side in the Y-axis direction, positive upwards in the Z-axis di-rection. The global coordinate system is used to describe the direction and velocity potential of the inci-dent wave. The origin of the local coordinate system OX;YZ; is located at the center of gravity of thefloating-body system separately, and the right-hand screw rule is required to abide by. The local coor-dinate system is used to describe the size of each floating-body system and its motions in the six degreesof freedom, including surge, sway, heave, roll, pitch and yaw.According to wave energy spectrum theory, irregular wave can be decomposed into several regularwaves, and n frequencies of regular incident waves can be obtained, namely w;，i = 1,,n. Twofloating-body systems have twelve degrees of freedom, namelyuk= {u气u气u峰u4 u峻峪T,k= 1,2(1)where ul ~峪denote six degrees of fredom for the k-th floating-body system, namely surge, sway,heave, roll, pitch and yaw. The equation is described as:之[-。w?(Ms+ A) + iow;(Cs+ B) + Kw+ K]]u= Fe(2)In the above equation, Ms is mass matrix, 12x 12; A is the added mass matrix, 12x 12; B isthe damping cofficient matrix, 12x 12; Kw is the restoring force coefficient matrix, 12x 12; F。rep-resents the exciting forces, including the first-ord中国煤化工rd second-order mean anddifference frequency forces. The above coefficie:MHCNMHG3D diffraction/ radiationpanel program WAMIT (Lee，1999). Cs denotes vIscous damping, and can be obtained from experi -ment or empirical formula. KL is stiffness matrix of hawsers, which depends on the material character-istics of connecting ropes. Finally the motions of six degrees of freedom for two floating-body systems inirregular waves are obtained.194TAN Zhen-dong et al . / China 0Ocean Engineering ，24(1), 2010, 191- 1984. Relative Motion Between Connectors of the Systems .Given EL as radius vector, which is between the center of gravity and connector of pontoon system1 and Es as radius vector in pontoon system 2. Then E.+ QL+ 0Lx E is the motion trajectory ofconnector of pontoon system 1 in the local coordinate system, and Es+ Qs+ θsx Es is the motion tra-jectory of connector of pontoon system 2 in the local coordinate system. Furthermore, the distance ofthe two connectors with time can be obtained by identifying the relative positions of these two connec-tors. Where QL and Qs respectively signify translational motion of the two pontoon systems; θ and θsrespectively signify rotary motion of the two pontoon systems .5. Simulation Model and ResultsIn consideration of the safety of pontoons' connection ，operations of modules were carried out un-der the third sea state conditions. The significant wave height is 1.0 m, the period was 3.68 s, thewater depth was 8. 0 m, and incident wave angle was0°, 30%， 60°, 90°，120°, and 150°， respective-ly. A certain connecting status was discussed ，which was that the connection of three standard modulesand three head-tail modules. The formner was tied to the tug tightly, without relative motion and thewhole system can be referred to as pontoon system 1. The latter was tied to another tug tightly, withoutrelative motion, too, and the whole system can be referred to as pontoon system 2.The global and local coordinate systems are shown in Fig. 2. The mesh model for hydrodynamiccalculation is shown in Fig. 3.n M,TugUnit 2Y2bxUnit 1M2②Fig. 2. Coordinate system of connecting state.Fig. 3. Mesh for hydrodynamics calculation.The displacement difference between the first pair of connectors with time is calculated, and theresults are shown in Table 1.From the above analysis, some useful concl中国煤化工lows: when wave angle is90°，the relative motion is the least, and it is:YHC N M H Gntoon connection. Whenwave angle is 150°， the relative motion is most obvious, and it is the worst sea condition for pontoonconnection.TAN Zhen-dong et al . / China 0Ocean Engineering ，24(1), 2010, 191- 198Table 1Distance between connectors through which steel rope 1 drillsThe statie distance is 1.0 mWave angleX-direction (m)Y-diretion (m)Z-direction (m)(°)MinimumMaximum00.871.13.-0.130.15- 0.85 ;0.82300.661.330.80- 1.101.03501.201.23900.991.01-0.350.38-0.390.421200.681.32-0.510.59-0.831500.631.42-0.820.78- 1.091.16The static distance is 2.0 mY-direction (m).1.862.140.14-0.790.77.1.662.33- 0.760.79- 1.061.812.21-0.840.83- 1.291.24)01.992.000.39.1.652. 32- 0.560.67- 0.840.861.632.411.176. Implementation of Dynamic Visualization by Visual FORTRANThe relative motion of two pontoons is calculated by Visual Fortran programming, and interface isdesigned by use of OpenGL. Thus , dynamic simulation of the connecting process is implemented. Theunderwater parts of Pontoon models are obtained from the data of finite element mesh directly. Thetransfinite interpolation scheme is applied for the mesh generation of the wave surface, where the finegrid is near the body and the coarse one is far from it, which can better reflect the floating body's per-turbation efects on the surrounding flow field. The wave motion is simulated by surface elevation,which is calculated by 3-D potential flow theory .6.1 Application of Infinite Interpolation TheoryThe coordinate data of the points on static water surface are obtained from the grid of the wettedsurfaces of the two pontoons, and then the gids of the suroundino wave surface are computed by inter-polation schemes. Yet， multidimensional grids中国煤化工rional iteplaion, withadoption infinite interpolation theory. The theoreTYHCNMHGf(u,u) is a two-variable function defined by a group of intersection curves M x N, and Ti, T2are given as follows.、MT(u,1) = >pm(u)f(um,r)(3)m=1196TAN Zhen-dong et al . / China 0Ocean Engineering ，24(1), 2010, 191- 198T2(u,n) = 2φ(v)f(u,0n)(4)where 9m and中。are combined functions and satisfy the conditions as fllows:qm(u) = δml，m = 1,2,.,M l = 1,2,,M(5)φ(v) = δnu，n = 1,2,..,N l = 1,2,.,NThe interpolating function TI fitsf on the boundary, u= u,.,uly，and the interpolating func-tion T2 fits f on the boundary v= Uy,"',0N.Substituting Eq. (5) into Eq. (3) and Eq. (4) forms the function W, as expressed in Eq. (6)、"W(u,u) = 2qm(u)f(um,u)+ 2中(v)f(u,n).(6)On the boundary u= um，W can be written as:W(um,v) = f(um,1)+ 2中(v)f(um,on).(7)n=1Because of the second formula，W can not fit the value on the boundary u = um，and the bound-ary v= Dn. Therefore, it is necessary to subtract a difference function R from W, R is expressed as ,follows:R(u,v) =m=l n=1gm(u),(v)f(um,0n).(8)The function W- R can fit all boundaries ,W(u,o)- R(u,u) =Pm(u)f(um,v) +之中φn(v)f(u,Un)m= 1n= 1艺之φm(u)中,(n)f(um,on).(9)m=1 n=1The function is called infinite interpolation function, because this function is in coincidence withthe whole boundaries rather than some isolated points, which is shown in Fig. 4.Fig. 4. Transfinite intepolation.f(mgy)中国煤化工MYHCNMHG6.2 Dynamic SimulationTo implement the interface between data results and 3D- Animation, the OpenGL commands canbe callede. Regarding the floating body as rigid body, two pontoons' relative motion can be counted asmulti-rigid motion. Then the origin of local coordinate system will be set at the center of gravity. Com-TAN Zhen-dong et al . / China 0Ocean Engineering ，24(1), 2010, 191- 198197pared with the sine wave, the simulation is more accurate and realistic. The dynamic efcts are shownin Fig. 5 and Fig. 6.Fig.5. Mesh for pontoons and wave surface.Fig.6. Simulation of relative motion.7. ConclusionsThe motion response of two pontoons in irregular waves is calculated by means of 3-D potentialflow theory. In addition, displacement difference of two connectors is obtained. And then the best stateand most dangerous state will be found in the connecting process, which provides exact basis for pon-toons connecting operation.The displacement difference of the two connectors provides data support for the designing shapeand size of connectors .Furthermore， Visual Fortran programming language and OpenGL ( Open Graphics Library) areused to simulate the relative motion. By use of the powerful computation capability of FORTRAN andgraphics library of OpenCGL, the animation is fully interactive with realistic efect.ReferencesChen, G. R. and Fang， M. C.，2001. 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(in Chinese)中国煤化工MYHCNMHG