On the effect of drag forces in mooring system restoring forces

Transcription

1 MATEC Web of Cofereces 138, 001 (017) CEF 017 DOI: /mateccof/ O the effect of drag forces i moorig sstem restorig forces Zahid Uah 1, Naik Muhammad 1, Ji-Hoo Lim 1, ad Dog-Ho Choi,* 1 Ph.D. Cadidate, Departmet of Civi ad Evirometa Egieerig, Haag Uiversit, Wagsimi-ro, Seogdog-gu, Seou, 04763, Repubic of Korea Professor, Departmet of Civi ad Evirometa Egieerig, Haag Uiversit, Wagsimi-ro, Seogdog-gu, Seou, 04763, Repubic of Korea Abstract. Moorig ie is a major source of stabiit ad pas a ke roe i the goba respose of offshore foatig wid turbie. I the curret state of the research, a formuatio based o the aatica catear equatio is most commo used for the aasis of moorig ies. However, due to the iabiit of catear equatios to cosider the ocea curret drag forces o moorig ies, the effect of drag forces o fairead restorig forces has ot bee ivestigated et. I this stud, we have ivestigated the ifuece of drag forces o fairead forces usig discrete catear formuatio for modeig moorig ie. The discrete catear formuatio has the abiit to icorporate ocea curret drag forces. Three tpes of eemets; fu suspeded, touchdow ad seabed eemet are formuated to mode the suspeded, touchdow ad seabed portio of a sack moorig ie, respective. The ifuece of viscous drag o the fairead restorig forces is demostrated through the aasis of OC3-Hwid moorig sstem subjected to ocea currets. It was foud that the viscous drag sigificat ifueces the fairead forces. 1 Itroductio The icreasig demad for epoitatio of reewabe wid eerg has dramatica icreased the size of the offshore foatig wid turbie ad pushed the istaatio of foatig wid turbie awa from shore i the deeper water. This deveopmet of offshore foatig wid turbie has resuted i the eed for more accurate aasis ad simuatio toos. Moorig ie pas a importat roe i the stabiit ad the goba respose of the foatig wid turbie. The accurate predictio of moorig oads ad fairead forces is ecessar for the safe desig of foatig wid turbie. Various umerica modes have bee proposed b various researchers for the aasis of moorig ies. The fiite eemet method has bee wide used for aasis of moorig ies [1-]. However, the high computatioa cost is a major weakess of the fiite eemet modeig. Due to computatioa efficiec ad easier impemetatio, the aatica catear approach has bee wide adopted b the various researcher [3-4] for the aasis of moorig ies. However, it is icapabe of takig ito accout the ocea curret drag forces. Therefore, the * Correspodig author: samga@haag.ac.kr The Authors, pubished b EDP Scieces. This is a ope access artice distributed uder the terms of the Creative Commos Attributio Licese 4.0 (

2 MATEC Web of Cofereces 138, 001 (017) CEF 017 DOI: /mateccof/ effect of ocea curret drag forces o the fairead forces has ot bee studied. The preset is stud focused o the ifuece of drag forces o the moorig ie restorig forces. Mathematica formuatio of moorig ie A improved quasi-static mode based o the discrete catear formuatio is used for the aasis of moorig ies. To mode the suspeded, touchdow ad seabed portio of a sack moorig ie three tpes of discrete catear eemets; suspeded, touchdow ad seabed are used, respective, as show i Fig. 1. The drag forces i vertica ad horizota directios are deoted b f ad f, respective; F 1 ad F deotes the fairead restorig forces i horizota ad vertica directios, respective; L ad L represets the horizota ad vertica projectios of the moorig ie, respective, ad w is the uit sefweight of the moorig ie. Fig. 1. Moorig ie aout ad discrete catear cabe eemets..1 Suspeded eemet The suspeded portio of moorig ie is modeed usig suspeded eemet. The horizota ad vertica projectio of a suspeded eemet ( i 1) ca be determied as: F1F s F1F s F1F F F (1)

3 MATEC Web of Cofereces 138, 001 (017) CEF 017 DOI: /mateccof/ F Fs F Fs F1F F F () where the s represet the ustraied egth of the eemet; F 1 i1 i i s f ad 1 i i Fz 1w fz s are the drag forces o the eemet i horizota ad vertica i1 directios, respective ad i represet eemet umber ( i 1 to N ).. Touchdow eemet The touchdow portio of moorig ie is modeed usig a touchdow eemet. The touchdow eemet is partia suspeded ad partia aig o the seabed. The suspeded portio of touchdow eemet is deoted b ps, ad the seabed portio of touchdow eemet is deoted b pb. The horizota ad vertica projectios of the touchdow eemet ( i ) ca be determied as foow: F1F f ps ps pb F1F f ps ps pb 1 F F f F F w f ps ps F F w f ps ps F F w f ps ps 1 F F f F F w f ps ps (3) (4).3 Seabed eemet I the sack cofiguratio of moorig ie, a sigificat portio of moorig ie is ig o the seabed. The seabed portio of moorig ie is modeed usig seabed eemets. The ustraied egth of a seabed eemet is deoted b b. The projectios of a seabed eemet ( i 1) ca be determied as foows: 1 1 ps F F f b (5) 0 (6) 3

4 MATEC Web of Cofereces 138, 001 (017) CEF 017 DOI: /mateccof/ Resuts ad discussios The ifuece of drag forces o restorig forces is ivestigated through the aasis of OC3-Hwid [5] moorig sstem subjected to a ocea curret. The moorig sstem cosists of three moorig ies. The diameter of a moorig ie is 0.09 m, moorig ie weight i water is N/m, ad the age betwee adjacet moorig ies is 10. Further detais are give i Tabe 1. Tabe 1. OC3-Hwid moorig sstem properties. Parameter Depth to fairead from mea sea eve Depth to achor from mea sea eve Radius to fairead from ceter ie of patform Radius to achor from ceter ie of patform Aia stiffess of moorig ie Vaue 70 m 30 m 5. m m N The OC3-Hwid moorig sstem is subjected to ocea curret of veocit.5 m/s. The age θ represets the directio of ocea curret with the respect to -ais. The foatig patform is quasi-statica dispaced from -4 m to +4 m i a swa directio. The ifuece of drag forces o the surge, swa ad heave restorig forces is demostrated i Fig. (a-c) for curret veocities V = 0,.5 m/s, ad θ = 0 o, 45 o. The figure shows that drag forces sigificat ifuece the fairead forces. The effect of drag forces o the surge ad heave restorig forces is more proouced. The effect of swa restorig forces is isigificat for θ = 0 o, however, the effect is icreased for θ = 45 o. The compariso of resuts aso demostrates that the et effect of drag forces o tota restorig forces depeds o the directio of ocea curret with respect to the orietatio of the moorig ies. For eampe, the effect of drag forces o heave restorig is isigificat for θ = 0 o, But for θ = 45 o the ifuece of drag forces o heave restorig forces icreased profoud. 4

5 MATEC Web of Cofereces 138, 001 (017) CEF 017 DOI: /mateccof/ Fig.. Restorig forces vs swa dispacemet (a) surge restorig force, (b) swa restorig force, ad (c) heave restorig force. 4 Cocusios This stud ivestigated the effect of ocea curret drag forces o moorig sstem restorig forces. The moorig sstem restorig forces pa a ke roe i the stabiit of foatig wid turbie. Moorig ies are modeed usig discrete catear cabe eemet. The effect of drag forces o moorig sstem restorig forces is ivestigated through the aasis of OC3- Hwid moorig sstem. It was foud that the drag forces sigificat ifuece the moorig sstem restorig forces. The effect of viscous drag forces i a specific directio i.e. surge, swa ad heave depeds o the directio of ocea currets with respect to moorig ies. This research was supported b the Basic Sciece Research Program through the Natioa Research Foudatio of Korea (NRF), fuded b the Miistr of Educatio, Sciece ad Techoog (NRF- 015R1D1A1A ). The authors wish to epress their gratitude for this fiacia support. Refereces 1. N. Haritos, D. He, Modeig the respose of cabe eemets i a ocea eviromet, Fiite eemets i aasis ad desig, 11, 19-3, (199). Z. Ra, M. Kim, Noiear couped resposes of a tethered spar patform i waves. Iteratioa Joura of Offshore ad Poar Egieerig, 7, , (1997) 3. R.P. Sigh, J. Verma, Evauatio of force-dispacemet reatioship for muticompoet moorig cabe b F.E.M., Computers & Structures, 30, , (1988) 4. JM. Jokma, Damics modeig ad oads aasis of a offshore foatig wid turbie, ProQuest; (007) 5. JM. Jokma, Defiitio of the foatig sstem for phase IV of OC3, Natioa Reewabe Eerg Laborator Gode, CO, USA, (010) 5