Design of Single-Point Mooring System with Moored Buoy

Transcription

1 7 th Internatonal Conference on Mechancs and Mechatroncs (ICMM 7) ISBN: Desgn of Sngle-Pont Moorng System th Moored Buoy Jun WANG a, Y ANG, Zhu-Yuan YANG and Yu-Me SHE School of Mathematcs & Computer Scence, Yunnan Mnzu Unversty, Kunmng, Yunnan, Chna Abstract. he sngle-pont moorng system s currently under a de range of applcatons n marne engneerng, marne observaton, marne farmng and other engneerng felds. So ths paper ntends to nvestgate nto the snglepont moorng system th moored buoy that s made up of a buoy, four steel ppes, a steel drum, a heavy ball, an anchor chan and an anchor. he am here s to desgn a sngle-pont moorng system mentoned above, hch can be used off shore. Namely, the follong parameter values have to be determned: the type and length of chan, the mass of compact ball, such that do not only both the buoy draught and the movng range, but also the vertcal angle of steel drum reach as small as possble. For the above purpose, frstly, analyse each component of ths system by means of the statc force method. Secondly, establsh a mathematcal model to calculate under the dfferent nd speeds all the mportant parameters, ncludng the vertcal tlt angle of the steel drum, the horzontal tlt angle of each steel ppe, the buoy draught, the buoy movng range and the chan shape. hrdly, on the bass of the above ork, a mult-objectve programmng model s establshed to obtan the desgn schemes n the dverse envronmental condtons nvolvng nd speed, seaater velocty and sea depth. Fnally, by smulaton t has turned out that these desgn schemes obtaned above are reasonable and applcable. herefore, they have defnte theoretcal sgnfcance and practcal values. Introducton he sngle-pont moorng system th moored buoy s one of the systems studed earlest by people. And t s used dely n marne engneerng, marne observaton, marne breedng and other felds because of ts smple structure, good drecton and lo cost. At present, the study on sngle-pont moorng system th moored buoy focuses manly on to aspects: the computatonal analyss of and the stablty of system. he former manly consders tenson response of moorng cables and couplng moton of moorng system. When computatonal analyss s performed on the cables, they are generally recognzed as a flexble structure, no thstandng shear stress, thereby no transmttng torques. he latter studes manly the bfurcaton and chaotc moton of system and other dynamc problems. he computatonal analyss can be subdvded nto the statc method and the dynamc method. he statc method [] neglects the nertal force of moorng system and nvolves catenary method, neutral buoyancy cable method, polygon approxmaton method, etc. Smth et al. [] used the catenary method to do the statc analyss to the moorng system that ncluded to cables. herefore, they converted the computatonal problem nto solvng a mult-degree-of-freedom polynomal equaton, hch could be solved quckly by computer. Pan et al. [3] proposed the to-dmensonal statc model for a sngle-pont moorng system th moored buoy, n hch the deformaton of moorng lne and the change of seaater flo speed ere consdered. a Correspondng author: angjun93484@63.com Hoever, ths model as only effectve on catenary, sem-tensoned and tensoned sngle-pont buoy systems. Wang [4] establshed the to-dmensonal statc model for underater submerged buoy system, on hch the effect of seaater flo as consdered but on hch the effect of the elastc deformaton of cable as neglected. By the statc equlbrum, the author calculated some parameters such as seaater depth, tenson, and nclnaton tlt angle, horzontal offset and so on, and developed the calculaton softare for system desgn and deployment. ang et al. [] used centralzed mass method for modellng and proposed the calculaton method of moorng tenson for deep ocean moorng system. hs method consdered gravty, buoyancy, tenson, ater current force, submarne support force etc. he results shoed that the greater change of the seabed topography had a certan nfluence on the tenson of the moorng lne. Lan et al. [6] descrbed n detal the statc calculaton steps and methods of submerged buoy system, and posture analyss. hey consdered the elongaton of cable, establshed a three-dmensonal statc model, and ponted out that the depth of the submerged buoy system had to teratvely calculate. Zhang et al. [7] calculated the tenson-span curve for each anchor lne based on one dmensonal optmzaton thought and the catenary equaton method. And the restorng force of moorng system as calculated by Lagrange nterpolaton method. Hoever, ths model as only applcable on catenary and sem-tensoned sngle-pont buoy systems. Wang [8] 97

2 appled the polygon approxmaton method based on the concentrated mass on the statc analyss of cable snglepont moorng system and establshed the statc model. hey took nto account the elastc stffness of the cable, analysed the stress characterstcs of typcal system components, ncludng buoy, and establshed the statc equlbrum equaton. For the ntal condtons of uncertanty, the teraton method as used to desgn the calculaton flo, and the statc calculaton program as programmed. he feasblty of ths method as verfed by the statc calculaton of a loose type sngle pont buoy system. Subsequently, the moorng system as carred out dynamcs analyss and modellng. Wang et al. [9] studed the deep-ocean sngle-pont moorng system th moored buoy, performed the statc analyss, and establshed the statc model n hch the change of seaater flo speed th the depth of the ater as taken nto account. Recently, some researchers [-3] bult up the dynamcal models for all knds of moorng systems to analyse ther nonlnear dynamcal propertes because of the actual requrements of engneerng. In ths paper, an offshore sngle-pont moorng system th moored buoy s nvestgated. It s made up of a buoy, four steel ppes, a steel drum, a heavy ball, a chan and an anchor. he am here s to determne the type and length of chan, and the mass of heavy ball to ensure the buoy draught, the buoy movng range and the vertcal tlt angle of steel drum are all as small as possble. For ths purpose, the statcs analyss s done to the above system by statc method, meantme consderng the nd speed, the seaater speed and the moment of force generated by four steel ppes and steel drum. hen, to obtan the optmal desgn schemes, construct a fe mathematcal models to analyse and optmze all knds of parameters, ncludng the buoy draught, the buoy movng range and the vertcal tlt angle of steel drum. In the end, t s verfed by smulaton that our obtaned desgn schemes of sngle-pont moorng system th moored buoy are both reasonable and applcable; thereby they have a certan practcal sgnfcance and reference value. he Components of System. Descrpton of the System Investgated he seaater depth of the offshore observaton netork s beteen 6m to m. Its transmsson nodes are composed of buoy, moorng and underater acoustc communcaton systems. he buoy system s smplfed to a cylnder th mass kg, bottom dameter m and heght m. he sngle-pont moorng system th moored buoy conssts of four steel ppes (for short ppe belo), a steel drum (for short drum belo), a heavy ball (for short ball belo), a elded chan (for short chan belo) and an ant-drag anchor (for short anchor belo). Each ppe s m long, mm n dameter, and kg n mass. he anchor s 6kg n mass. Usually, a chan uses common chan lnk to connect. Its types used often and the parameters are shon n able. If the angle beteen the seabed and the tangental drecton of chan at ts end does not exceed 6, the entre moorng system ll stay there thout movng. Otherse, the anchor ll be dragged such that the nodes are shfted and hence lost. he underater acoustc communcaton system s nstalled n a sealed cylndrcal drum hose length and dameter are m and 3cm respectvely, and the mass of the hole devce s kg. he top of drum s connected th the 4th ppe and ts end s connected th the chan. If the drum s n a vertcal state, the underater acoustc communcaton system orks best. If t s tlted, the effect of communcaton system gets orse. As the angle beteen t and the vertcal lne (referred as vertcal tlt angle) exceeds, the communcaton system orks very poorly. In order to control the sze of vertcal tlt angle, e can hang a heavy ball at the juncton of drum and chan (See Fgure ). ype able. Chan types and parameters. l (mm) (kg/m) ype l (mm) (kg/m) I IV 9. II 7 V 8 8. III. Note : he length refers to the one of each chan lnk. 6m m Anchor Anchor Chan Sea Level Seabed Steel L 3 3 L 4 L 4 Steel Drum Buoy L Vertcal Lne Heavy Ball Fgure. he system studed and some symbol descrptons.. Symbols Descrpton For the convenence of smplcty, some symbols need to be ntroduced. he meanng and ts unt of every symbol (f t exsted) are shon n able..3 Fundamental Assumptons For the sake of smplcty, e gave the follong fve fundamental assumptons. Hypothess : As the moorng system reaches a statc equlbrum, the buoy, 4 ppes, drum, ball, chan and anchor are all n the same plane. Hypothess : he volumes of chan can be neglgble, hence both ts buoyancy and ater current force are zero,.e., F6 A6. Hypothess 3: F.6 v S(N) approxmately. Here, S (m ) s the projected area of object on the plane L 98

3 perpendcular to the nd drecton, and nd speed. v (m/s) s the able. Symbol descrptons. Symbol Unts Meanng g m/s he gravtatonal acceleraton, g 9.8. H m he ater depth. 3 kg/m he sea ater densty,. 3. kg/m he lnear densty of chan. A c N he current force. A N he ater current force actng on ball. A~ A 7 N he ater current force actng on the buoy, the st~4th ppe, drum, chan and anchor n sequence. m m m m. m~ m 7 kg he mass of the buoy, the st~4th ppe, drum, chan and anchor n sequence, th 3 4 G~ G 7 N he gravty of the buoy, the st~4th ppe, drum, chan and anchor n sequence. F~ F 7 N he buoyancy of the st~4th ppe, drum, chan and anchor n sequence. L L m he lengths of the st~4th ppe and drum n sequence, th L = L, ~. D D m he dameters of the st~4th ppe and drum n sequence, th = ~ D = D D3 = D 4. ~ he horzontal tlt angles of the st~4th ppe and drum n sequence. P, Q, P he locatons of the top (, ) x y, the end (,-H ) and arbtrary pont ( xy, ) of chan respectvely.,, he angles of the sea level and the tangental lne at P, P, Q respectvely. ss, m he lengths of chan from Q to P and to P respectvely, s l. hr, m he buoy draught and the buoy movng range respectvely. H, D m he heght and dameter of buoy respectvely. 6, N he pullng force of drum actng on chan and on ball respectvely. GF, N he gravty and buoyancy of ball respectvely. N he pullng force of chan actng on anchor. 7 vu, m/s he nd speed and seaater current speed respectvely. N ( xy, ) he tenson of chan at P. N he pullng force of buoy actng on the frst ppe. N he pullng force of the (-)-th ppe actng on the -th ppe, 4. N he pullng force of the 4-th ppe actng on drum. he acute angle formed by the lne on hch les and the sea level, 4. 99

4 he vertcal tlt angle of drum,. F ( h ) N he buoyancy of buoy, t s a functon th respect to h. F N he nd force actng on the buoy. l m he length of chan. m he length of chan lyng don on the seabed. m kg he mass of ball. S m he projected area of the object n the normal plane. y f ( x) he shape of chan. sn, Hypothess 4: A 374 u S(N) approxmately. Here, c S (m ) s the projected area of object on the plane perpendcular to the ater current drecton, and (m/s) s the seaater flo speed. Hypothess : Ocean current s a planar flo feld, and u does not change th the ater depth; hence, t s a constant [9]. Hypothess 6: he gravty of ball s much larger than ts buoyancy and ater current force. So, ts buoyancy and ater current force can be neglgble,.e., F A. Hypothess 7: he ater current force of each component acts on ts centrod..4 he Establshment of Coordnate System As s shon n Fgure, a planar coordnate system s establshed. Accordng to Hypothess, there exsts the plane here the system reaches the statc equlbrum state. We take t as the coordnate plane. ake the ntersectng lne of the coordnate plane and the sea level as the -axs hose postve drecton s just the nd drecton. And the Y-axs, hose postve drecton s just stckng straght up, passed through the jont of anchor and chan and s perpendcular to the - axs. he ntersecton of the -axs and Y-axs s the orgn denoted by O. H Y Anchor y x R Sea Level Anchor Chan h p x, y Seabed Buoy. Desgn Process Step : ransmsson node uses ype of chan hose length l.m and the mass of ball m kg. he anchor s placed on the flat seabed here the ater depth H 8m and ts densty 3 3. kg/m. Assumng that u, construct a model to calculate all the parameter values hr,,, and determne the shapes f( x ) of chan as and v 4m/s respectvely. v m/s Step : Accordng to Hypotheses -7, calculate all the parameter values hr,,, and determne the shapes f( x ) of chan as v 36m/s. If the anchor s dragged or the communcaton system orks poorly, then adjust the mass of ball m, satsfyng the condtons that & 6. Step 3: he devce s placed n the sea here the ater depth s beteen 6m and m and the maxmal ater current speed u.m/s and the maxmal nd speed v 36m/s. he desgn scheme of moorng system s gven accordng to dfferent nd speed, ater current speed and seaater depth. Step 4: Smulaton. For the desgned moorng system, smulate the statc equlbrum system n the follong three cases of v, 4,36m/s respectvely and u.m/s. Namely, determne the reasonablty of the parameter values hr,,, and the shapes of chan n the three cases above, as the moorng system s equalzed. Subsequently, verfy hether the parameters meet the demands of objectve realty. If not, the desgn scheme ll be redesgned. Fgure. he coordnate system.

5 3 he Implementaton of Step he force analyss of each component s done and then ther force and torque equlbrum equatons are acheved by the above fundamental hypotheses. And so they consttute a system of equatons, through hch the expressons of h, R,, ( 4), and ( ) f x can be deduced. Model s constructed usng these expressons. hen Model s solved and all the parameter values of hr,,, and ( ) f x s obtaned under dfferent condtons. No let s begn th the force analyss on each component. L F C G Fgure 4. Force analyss of the frst ppe. 7 F 3 3. Force Analyss of Each Component G C 3.. he Force Analyss of Buoy, Ppe and Drum (Includng Ball) By Hypotheses and 6, and Fgures 3-, the force equlbrum equatons of the buoy, 4 ppes ( 4) and drum are respectvely obtaned as follo. sn F ( h) G () cos F () sn sn G F (3) cos cos (4) sn sn F G G () 6 cos cos (6) 6 Further, select respectvely as the fulcrum the centrod C of each ppe and of the drum. hen by Hypothess and Fgures 4-, ther torque equlbrum equatons are also respectvely obtaned as follo. sn( ) sn( ) (7) sn( ) sn( ) G cos (8) 6 Wnd Drecton F h 6 7 G 6 Fgure. Force analyss of drum and ball. 3.. he Global Force Analyss of Chan he force of chan can be analysed accordng to the follong to cases:, ; (),. s l By Fgure 6, t follos that. So by Hypothess, the chan has the follong global force equlbrum equatons. sn sn g( l ) (9) 7 6 cos F () 3..3 he Local Force Analyss of Chan By Fgure 7, the local force equlbrum equatons are got as follo. x, () s y dx s l gs 7 sn ( xy, ) sn () 7 cos ( xy, ) cos (3) h Sea Level F y H, y tan (4) x x Note : If, then. G Fgure 3. Force analyss of buoy.

6 7 7 s gs, 6, P x y 7 s gs, Fgure 6. he global force analyss of chan. gs, s x, y P x, y 7 s, Fgure 7. he local force analyss of chan. gs 6 P x, y x, y P x, y x t t x C: C : y H y t H t l (b) Case : v. hen, F. So t has the follong system of equatons. hh 4 F F F ( H ) g G 4G G G G 6 / 4 gd.6tan Dv (9) arctan F, 4 () F G F arctan () 3. Some Basc Relatons By Hypothess 3 and some basc physcal knoledge, the follong basc relatons hold. F D H h v.6 ( ) () F ( h) 4 gd h (6) F 4 gd L, (7) G m g, ; 6 6 G m g gl, G mg 3.3 he Establshment of Model and the Results on Soluton 3.3. he Expresson of Relevant Parameters (8) By Equatons s l and () (8), the expressons of h, R,, ( 4) and the shape f ( x ) of chan are obtaned mmedately. Let s dscuss them as follo. (a) Case : v. At ths tme, F. It can be seen easly that ( 4) and. So, t has the follong results : m 4m m m l 4 D L l 4D L D L D H 4 D h H L l R And the shape f ( x ) of chan s composed of the follong to lne segments C and C. () y h L sn (3) a g F (4) ( sec ) tan s a ay ah () x l s (6) (tan sa) tan s ln a a sec tan (7) cos (8) R L x, ;, (9) H, x ; sec cosh a ( x ) a y tan snh a ( x ) x x a sec H, a Note 3: sn ( ) Equatons () and (3). can be obtaned by (3)

7 3.3. he Establshment of Model No, only consder the case v. Combnng Equatons (), (3), (), (6) and (9) ~ (3), Model s obtaned he Soluton of Model For Model, usng the step-search method, solve all the parameter values h, R,, ( 4) as the moorng system s equalzed under dfferent nd speed. Further, one can ascertan f ( x ). So, one has the follong concluson. he moorng system does not shft as v m/s and v 4m/s respectvely. At ths tme, all the parameter values are shon n able 3, and the shapes f ( x ) of chan shon n Fgure 8. 4 he Implementaton of Step 4. Determne the State of Moorng System 4.. he Condton for Moorng System n Statc Equlbrum State he necessary and suffcent condton that the moorng system reaches a statc equlbrum state s 4.. Determne the State of Moorng System s l. Assumng that the moorng system s n a statc equlbrum state as v 36m/s, employ the ay used n Model and fnally get & s l.648, hch does not meet the condton of moorng system n statc equlbrum state. able 3. he results of Model ( v m/s and v 4m/s ). v (m/s) 4 v (m/s) 4 hm ( ) ( ) Rm ( ) ( ) () ( ) ( ) Fgure 8. he shapes f( x ) of chan ( v = m /s,v = 4 m /s ). 4. Determne the Best Mass of Ball 4.. he Establshment of Model Accordng to the above force analyss, gettng a model determnng the smallest mass of ball, hch s shon belo, called Model. mn G F h G 4G G G 6 F tan 4F F g st.. 6 m M, G mg (),(3),(),(6),() (8) (3) ake M as the stop condton for the stepsearch algorthm solvng Model. 4.. he Soluton of Model As v 36m/s, the least mass of ball should be 8.7kg, and at ths tme, and he other parameter values are shon n able 4. able 4. he results of Model ( v 36m/s ). v (m/s) 36 v (m/s) 36 v (m/s) 36 h (m).94 ( ) ( ) 8.44 R (m) 8.48 ( ) ( ) 8. he Implementaton of Step 3 the Desgn of Moorng System he desgn of the moorng system s to determne the type and length of chan, and the mass of ball, such that not only do the buoy draught and movng range reach the mnmum, but also the vertcal angle of drum do so f the 3

8 moorng system s n an equlbrum state. herefore, t s a mult-objectve programmng problem. Based on practcal applcatons, the ater current force has to be taken nto account n the system desgn. So, t s necessary to make the follong modfcaton on the force equlbrum equatons of the buoyant, the drum, and all the ppes... he Modfed Equaton.. he Force Equlbrum Equatons of the Buoyant, 4 Ppes and the Drum here beng the ater current force,.e., u, so, accordng to Hypotheses -7, only the horzontal force equlbrum equatons of the buoyant, the 4 ppes and the drum,.e., Equatons (), (4) and (6), have to be modfed as follo. Here, cos A F (3) cos cos A, 4 (33) cos cos A (34) 6 A 374Du h (3) A D u L (36) 374 sn,.. Modfcaton of the Correspondng Equatons Because of Equatons (3), (33) and (34), the other correspondng equatons have to be modfed as follo. F A A A 4 arctan, F G arctan F A A A g a F A A A G F H G 4G 4F F G tan F A G g 6 (37) (38) (39) (4) G 4G G G6 G 4F F h 4 gd.6 tan Dv 374 tan Du g tan.6hdv A. he Establshment and Soluton of Model 3... he Establshment of Model 3 (4) A mult-objectve programmng model s bult up as follos. st.. mn h, mn &mn R 6 (),(3),(),(6),() (8),(3) (4), h s Accordng to Equaton (4), for any gven ncreasng th respect to G. Smlarly, for any gven G, h s ncreasng th respect to as v 36m/s & u.m/s. So, convert the mult-objectve programmng to the follong sngle-objectve programmng. mn G R W M 6 M st.. 6 (),(3),(),(6),() (8),(3) (4) M & M 4. Here, take 6.. he Soluton of Model 3 and the Desgn Schemes of Moorng System Due to, t has sn and hence, A D u L. It means that the nfluence 374, of on A can be neglgble ( ). Set v 36m/s and u.m/s n Model 3. If H 6,7,8,9, m respectvely, and 3.,7,., 9.,8.kg/m, then stll use the step-search method to solve Model 3. Fnally, get sub-optmal solutons of Model 3 under the above knds of cases. Select optmal solutons from them as the desgn schemes of moorng system, hch are shon n able. 4

9 able. he desgn schemes of moorng system. H (m) (kg/m) ype V V V V V l(m) m(kg) h(m) () R(m) he Smulaton In order to verfy the theoretcal desgn schemes n able, the smulaton s done to observe all the parameter values as u.m/s and v,4,36m/s respectvely. Here, t should be ponted out that n the smulaton, the changes of ater current force actng on the 4 ppes and the drum are not taken nto account, and that they are regarded as the maxmum values of ther on ater current forces nstead. Here, the shapes of chan at dfferent speeds are shon n Fgure 9 respectvely for the seaater depth 6m n the desgn scheme. Fgure 9. he shapes f( x ) of chan. ( v m/s, v 4m/s& v 36m/s ) Conclusons Under the same seaater depths, all the parameters meet the practcal requrements, judgng from all the obtaned parameter values, ncludng the shapes of chan, at dfferent speeds based on the above smulaton. So, from the ve of statc analyss, the smulaton results have shon that the theoretcal desgn schemes of moorng system n able are reasonable and applcable, even f the hurrcane reaches to 36m/s and the seaater current does.m/s. So they have a certan practcal sgnfcance and reference value. References [] Berteaux H. O. Buoy engneerng. [M]. 976, Ocean Engneerng, Wley. [] Smth R. J., Macfarlane C. J. Statcs of a three component moorng lne. [J], Ocean Engneerng, 8(7): [3] Pan B., Gao J., Chen., Chen J., Statc calculaton of marne submersble buoy system. [J]. Journal of Chongqng Jaotong Insttute (Natural Scence Edton), 997, 6(): [4] Wang M. Statc analyss and atttude calculaton of marne submersble buoy system [J]. Journal of Oceanc echnology,, (4):4-47. [] ang Y., Y C., Zhang S., and Analyss of cable shape and cable tenson for platforms n deep sea. [J]. Ocean Engneerng, 7, ():9-4. [6] Lan Z., Yang S., Lu L., Gong D., L S., Zhu S., he desgn and atttude analyss of a subsurface buoy for deep sea current proflng. [J]. Marne Scences, 8, 3(8):-4. [7] Zhang H., Zhang., Yang J., Statc characterstc analyss of mult-component moorng lne based on optmzaton thnkng. [J]. Shp Scence and echnology,, 3():4-. [8] Wang L., Study on dynamcs of sngle-pont moorng systems. [D]. Ocean Unversty of Chna,. [9] Wang Y., Study on the sngle pont moorng of ocean buoy n Deep Ocean. [D]. Ocean Unversty of Chna, 3. [] u J. P., he three-dmensonal dynamc analyss of moorng system and expermental study on t. [D]. Ocean Unversty of Chna, 4. [] Zheng Z. Q., Study on nonlnear dynamcs of Marne moorng systems. [D]. Ocean Unversty of Chna,. [] Wang B., ang J., Hu W., Desgn of anchor moorng system based on Hong Kong-Macao tunnel s layng and transportaton ork [J], Logstcs Engneerng and Management, 6, 38(). [3] Pan S. H., Wang S. Q., Lu L. Z., he optmal desgn of moorng system based on the equvalent depth truncaton of the platform rotaton [J], Ocean Engneerng, 7(). Acknoledgement hs ork s fnancally supported by Natonal Natural Scence Foundaton Projects (64696&3676), Yunnan Provncal Department of Educaton Scence Research Fund Project (6YJS78), and Yunnan Mnzu Unversty Overseas Master s Program (399).