A Combination Mooring System and Mooring Characteristics Study

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(1.Harbin Engineering University,Harbin 150001,China;2.Nanjing Communications Institute of Technology, Nanjing 211188,China)

A Combination Mooring System and Mooring Characteristics Study

ZHANG Liang1,LI Hui1,MA Yong1,ZHANG Wei1,DU Cheng-ren2

(1.Harbin Engineering University,Harbin 150001,China;2.Nanjing Communications Institute of Technology, Nanjing 211188,China)

To further reduce the motion of floating body,a combination mooring system is selected in application.Based on the 3-D potential theory,the motion of a moored floating body is calculated by using AQWA software.And the mooring system is composed of chain,clump,elastic cables and combination of them.By comparing the floating body response and tension in fairlead,this paper finds that the motion and tension are reduced largely when the mooring system contains elastic cables.The motion and mooring line tension decrease further when the length of elastic cable increases but the position of the elastic cable makes no difference to the motion and the tension.In addition,the motion reduces when the mooring system contains clump,but the tension increases a little,which has very important significance in practice.

mooring system;potential theory;elastic cable;clump;AQWA

0 Introduction

In ocean engineering,the floating structure mainly adopts two kinds of positioning system, mooring system and dynamic positioning system.Mooring system has many advantages such as less investment,convenience and easy maintenance,so it is the main positioning system at present.Traditional catenary mooring system composed of steel chain or wire rope is usually only applied to 1 000 m depth.When the depth exceeds 1 000 m,not only does its cost increase,but also brings great weight to structure.Because the restoring stiffness of the system decreases with the increase of the depth,the platform in extreme weather conditions has great horizontal deviation,and the design and construction confront many new problems.Therefore,in order to reduce the weight and cost,deep-water mooring system usually adopts combination mooring system.

Pan[1]studied the combination mooring system.As long as the design is reasonable,the total restoring force of the system is usually bigger than that of mooring system composed of all over ropes or chains when giving the same displacement.Yu,Li[3]studied the static prob-lem of chain-line-chain catenary mooring line provided no current and ignoring the line deformation.Catenary length was given in the form of implicit function equation from the calculation formula of bottom part of the length.The analytical expression of catenary shape and tension was given in the form of parametric equation.Ji,Yuan,et al[4]proposed a new mooring system composed of chain,polyester and clump.The comparison result between the new mooring system and the original system showed that the motion of the platform using the new type mooring system was smaller than that using the taut mooring system,which ensured a better working condition.

Based on this background,this paper proposes a new mooring system composed of elastic cable,clump and chain.Through comparing with the original mooring system,this paper finds the elastic cable can increase grounded chain,and the maximum of the tension can be reduced by 11.31%.Changing the elastic cable position almost has no impact on other degree of freedom motions and mooring forces except surge.When elastic cable length increases,the tension decreases rapidly and pitch appears minimum.For combination mooring system containing elastic cable and clump,clump weight not only decreases motion amplitude of the floating body,but also increases the tension in fairlead and the grounded chain length.Clump’s position in elastic cable has little effect on the motion of the floating body and tension.In the uniform current case,for the same weight of clump,whether one or more,the maximum difference between them is less than 2%,which has great advantages in practice.

1 Mathematical model

1.1 Introduction of theory

The floating body hydrodynamic parameters that AQWA can calculate mainly include the first-order wave forces,wave frequency radiation damping and added mass,mean wave drift force,and the calculation of these forces is mainly based on the 3-D potential theory.The floating body motion equation is expressed as:

where Mais the mass of floating body;A,B and K are the added mass,damping and stiffness matrix of the floating body,respectively;Fwaand Fmare wave forces and mooring force,respectively.

Fig.1 A three component mooring line arrangement

The complete submerged mooring line configuration is shown in Fig.1.The lower line connects to grounded catenary and anchor providing a horizontal restraint force.The upper line connects to a floating platform.The two lines are connected at a point buoy or clump.Loads on the mooring lines are the immersed self-weights of the components and end-point tensions. The lines are considered inextensible in the present description.Static equilibrium between the touchdown point at the origin of the axes x and y,and distance s along the mooring is given by the summation of forces

where vectors are denoted by boldface,t is the unit tangent in the direction of increasing s,f is the external load distribution and T is the tension.The load f is given by

where w1and w2are uniform immersed line weights per unit length,W1is a concentrated force at the connection point 1,and δ and H are the Dirac impulse and Heaviside step functions.Resolving Eqs.(2)and(3)along the directions of the axes x and y,gives

where

The horizontal component of the tension is constant along the mooring and represents the restraint force of an anchor positioned at s＜0.

Manipulation of Eq.(4)and Eq.(5)leads to the classical catenary equations(Symon,1971; Meriam,1975):

where the subscript i=1,2 for mooring lines on the intervals 0=s0≤s＜s1,s1≤s≤s2and αi,βiand γiare integration constants to be determined from boundary conditions.

1.2 Model parameters

Platform is a floating tidal power station,and essential characteristics of the platform are summarized in Tab.1.

Tab.1 Essential characteristics of the platform

The finite element mesh model is shown in Fig.2.For the full comparison between the mooring effect of the new mooring system and that of original mooring system,the same arrangement of mooring lines is adopted,as shown in Fig.3.There are 4 combination mooring lines.The schematic plot of the arrangement for mooring lines is shown in Fig.3.Each mooring line adopts chain and elastic cable,the axial stiffness of the cable is 1.0×109N/m,cable diameter is 69 mm.While elastic cable is nonlinear,i.e.the stiffness is associated with elongation.

Fig.2 The finite element mesh model

Fig.3 Arrangement of the mooring lines

2 Calculation and analysis

In this paper,the calculation is in the time domain.The selected wave spectrum is the Jonswap wave spectrum,in which the significant wave height is 4.0 m,the peak frequency is 0.63 rad/s.The simulation time is 3 hours with 32.7 m/s design wind speed and 3.3 m/s design current velocity.The wave,wind and current approach platform at angles of 0°.

2.1 The effect of elastic cable on platform motion and chain tension

This paper firstly studies the effect of elastic cable on platform motion.Fig.4 shows mooring system schematic plot,ED is grounded chain,ED,CD and AB are chain,BC is elastic cable.In this part,the total length of each line is 252.5 m,and BC=8 m,AB=5 m.

Tab.2 Floating body motion comparison with no elastic cable

Fig.4 Arrangement of elastic cable

Fig.5 Tension comparison

Fig.5 is a tension comparison curve,in which time is selected from 400 s to 460 s to express the curve more clearly.Tab.2 is a comparison of floating body motion,which only lists surge,heave and pitch for the motion amplitude of other degrees of freedom in 0°incident angle is small.From Fig.5,it can be seen the tension decreases significantly when containing anelastic cable.The main cause is that the addition of elastic cable reduces the vertical component of the tension,and the second cause is that the elastic cable makes the change of tension more smoothly.Seen from Tab.2,surge and heave amplitude increase when mooring system contains elastic cable.It is mainly because the stiffness of the system containing elastic cable is reduced.The wave forces remain unchanged,so the floating body motion increases.When stiffness decreases,the natural frequency of the system is changed,so the pitch decreases.As the platform is tidal power station platform,surge motion has little effect on its normal operation,and the pitch will have a large impact on the platform.Elastic cable not only reduces the chain tension,but also decreases the pitch.

In this part,the next is to study the effect of elastic cable position on the motion of the platform and the tension.The only variable is the distance along mooring line from the center of elastic cable to fairlead.Elastic cable length is 8 m;d denotes distance from elastic cable center to the fairlead along mooring line.The motion amplitude of roll,sway and yaw is very small in 0°wave direction,so Fig.6 only draws surge,heave,pitch and tension with different d.From Fig.6,it can be seen that as long as the elastic cable length does not change,changes of elastic cable position have little impact on the platform motion except surge.This is mainly because main parameters such as αi,βiand γi,are determined by boundary conditions for multicomponent mooring system,changing the elastic cable position just changes the tension distribution but boundary conditions almost have no change.So the fairlead tension has little been changed.

Fig.6 Floating body motion and chain tension with different d

When the elastic cable location does not change,Fig.7 draws pitch and tension with the variation of elastic cable length and l denotes the elastic length.It can be seen from Fig.7,cable tension decreases rapidly with the increase of elastic cable length.Compared to the no elastic cable case,the chain tension decreased by 6.13%with a 4m elastic cable,the chain tension decreased by 9.73%with a 7 m elastic cable,the chain tension decreased by 11.31% with 9 m elastic cable,while grounded chain increases by 2.35%.Because of its small mass, elastic cable reduces the vertical weight of the system.The more elastic cable length will increase,the more the vertical component force will decreases.On the other hand,elastic cable makes the transition more smoothly because of its small stiffness.It also finds that,with the increase of elastic cable length,platform pitch decreases at first and then increases,and reaches the minimum at about d=8 m.The mooring system can be approximated as rigid spring act-ing on the floating body,which is added to the floating body as additional linear stiffness.It affects the floating body natural cycle of pitch,which is far away from wave period.With the analysis above,we can choose appropriate elastic cable length,which further verifies the great advantage of elastic cable.

Fig.7 Tension and pitch with l

Fig.8 Arrangement of elastic cable and clump

2.2 The effect of clump position on platform motion and chain tension

Fig.8 shows mooring system schematic plot,ED is grounded chain,ED,CD and AB are chain,BC is elastic cable and C point hangs a clump.In this section,the total length of each mooring line is 252.5 m and BC=8 m,AB=5 m.When the clump weight is 500 kg,the effect of clump location on the motion of the platform and chain tension is studied.Case a represents the clump is located on B point and case b represents a clump located on C point.Because the motion amplitude of other degrees of freedom is relatively small,Tab.3 only lists the maximum of surge,yaw,pitch and tension.As seen from Tab.3,the motions of the platform are different with different clump positions in the chain.Specifically,compared with case a,surge,heave, and pitch of case b have increased by 0.04%,0.59%,0.75%,respectively.The maximum of tension increases 0.08%.The equations of multicomponent mooring lines show that the parameters αi,βiand γiare only associated with the boundary conditions.In the case above that elastic cable length is 8 m and the chain length is 252.5 m,change of clump position along the elastic length has little disturbance on boundary conditions,which leads to little change to the tension in fairlead.

Tab.3 The effect of clump position

When length of elastic cable remains unchanged,the effect of clump weight on the plat-form and mooring lines is studied.Because the wave direction is 0 degrees,other degrees of freedom changes are relatively small.Fig.9 only lists heave and pitch curves in which the elastic cable length is 8 m.It can be seen from Fig.9,pitch curve changes very smoothly while heave decreases slightly with the increase of the clump weight,and tension almost increases linearly with the increase of the clump weight.Heave damping increases because of the existence of the clump,which decreases the heave amplitude.But the clump weight is much smaller than the floating body,the damping is limited.So the heave reduction is relatively small. Since the floating body moored with four points,pitch angle is relatively small.Furthermore, the clump increases grounded chain,which is very useful in practice.

Fig.9 Motion and tension with different clump mass

2.3 The effect of clump weight distribution on the platform motion and tension

Tab.4 Motion and tension with different clump mass distribution

Firstly,the effect of clump weight distribution on the platform is studied.In this part,elastic cable length is 8 m and the center of elastic cable away from platform is 9 m.Case 1515 represents two 1.5 t clump hanged on the B,C.Case 051015 means 0.5 t,1.0 t and 1.5 t clump suspended on B,C and the middle of BC,respectively.Case 30 represents a 3.0 t clump located on the C point.Due to small changes in other several degrees of freedom,Tab.4 only lists surge,heave and pitch of the platform and tension at the fairlead.From Tab.4,comparedto the centralized clump case,the amplitudes of several degrees of freedom in the other two cases have changes,but the fluctuations are very small.Compared to the case 30,the tension of other two cases increases.In the calculation,the clump’s load calculated by Morison formula is different in different depths.The current velocity at the surface is large,and the velocity decreases gradually with the increase of depth,which leads to small current load.The tension of system at this time will reduce,which is proved by the above results.

3 Summary

Based on a tidal power station platform moored with a combination mooring system including clumps and elastic cables,this paper has made coupled analysis of platform and mooring system.The drawn conclusions are as follows:

(1)In the mooring system design of shallow water,elastic cable can reduce the chain tension mutation,reduce the stiffness of the system,increase the grounded chain length,and reduce tension.Mooring system containing elastic cable can reduce the platform pitch,at the same time surge and heave increase slightly.When changing elastic cable position,motion of other degrees of freedom and tension almost changes little except surge.When elastic cable length increases,the tension almost decreases linearly,and pitch has the minimum.

(2)For platform moored with elastic cables and clump,increase of clump weight not only decreases motion amplitude of the floating body,but also increases the tension in fairlead and the grounded chain length.Clump’s position in elastic cable has little effect on the motion of the floating body and tension.In the uniform current case,for the same weight of clump,whether one or more,the maximum difference between them is less than 2%.

In the mooring system design of shallow water,the combination mooring system containing elastic cables has great advantages in the practical engineering design and construction. The conclusions of this paper have very important practical significance.

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一种组合系泊系统及其系泊特性影响研究

张 亮1，李 辉1，马 勇1，张 伟1，杜成仁2

（1.哈尔滨工程大学 船舶工程学院，哈尔滨 150001；2.南京交通职业技术学院，南京 211188）

为了在较低的成本下更大程度地减小浮体的运动，文章提出了一种组合系泊系统的概念，并基于三维势流理论,当系泊形式为锚链、重块、弹性索以及它们之间的组合时，运用AQWA软件计算了系泊浮体在不规则波中的运动响应。在几种不同的工况下，通过比较浮体的响应和锚线张力，发现有弹性索时浮体运动和张力明显减小，当弹性索长度增加时，运动和张力减小得更多。当弹性索长度一定时，位置的变化对浮体运动和锚链张力响应不大。带沉子时浮体运动减小，同时锚链张力增加得也不多，文中的发现在工程使用中具有很重要的参考和借鉴意义。

系泊系统；势流理论；弹性索；沉子；AQWA

O352

:A

张 亮（1959-），男，哈尔滨工程大学船舶工程学院教授，博士生导师；

1007-7294（2016）03-0306-09

O352

A

10.3969/j.issn.1007-7294.2016.03.007

李 辉（1989-），男，哈尔滨工程大学船舶工程学院硕士研究生；

马 勇（1980-），男，哈尔滨工程大学船舶工程学院讲师，通讯作者；

张 伟（1990-），男，哈尔滨工程大学船舶工程学院硕士研究生；

杜成仁（1980-），男，南京交通职业技术学院讲师。

Received date：2015-08-18

Foundation item:Supported by the National Natural Science Foundation(51309069&11572094),Harbin Innovation Talent in Science and Technology Research Special Fund(2014QN001008)and Chinese Postdoctoral Science Fund(2014M561334)and Coupling Characteristic Analysis of Floating Wave-current Hybrids System(51579055)

Biography：ZHANG Liang(1959-),male,professor of Harbin Engineering University,E-mail:zhangliang@hrbeu.edu.cn

LI Hui(1989-),male,master of Harbin Engineering University,E-mail:huioffshore@163.com.