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Article(id=1243896355505161147, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243896350367134664, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2025.09.006, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1741881600000, receivedDateStr=2025-03-14, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774497601629, onlineDateStr=2026-03-26, pubDate=1758297600000, pubDateStr=2025-09-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774497601629, onlineIssueDateStr=2026-03-26, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774497601629, creator=13701087609, updateTime=1774497601629, updator=13701087609, issue=Issue{id=1243896350367134664, tenantId=1146029695717560320, journalId=1240685776644648972, year='2025', volume='29', issue='9', pageStart='1343', pageEnd='1498', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774497600404, creator=13701087609, updateTime=1774501609474, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1243913165692584796, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243896350367134664, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1243913165692584797, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243896350367134664, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1397, endPage=1406, ext={EN=ArticleExt(id=1243896356151083971, articleId=1243896355505161147, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Motion response of FPSO system under bimodal spectrum waves, columnId=1241023037940748650, journalTitle=Journal of Ship Mechanics, columnName=Hydrodynamics, runingTitle=null, highlight=null, articleAbstract=

The South sea of China is affected by tropical cyclones and typhoons in the western Pacific Ocean, which are prone to double-peak or even multi-peak waves in the form of mixed waves, which are potentially hazardous to the operational safety of marine floating structures. Therefore, based on the potential flow theory and considering the influence of different loading states, a comparative study was conducted on the motion response of FPSO and shuttle tanker side-by-side system under double-peak spectral wave and single-peak spectral wave states. The motion responses of the two hulls in the double-peak spectral wave states of mainly wind waves, wind waves and surge are equal, and mainly surge and the single-peak spectral wind waves state are calculated respectively. The calculation results show that (1) the amplitude of the motion of the two hulls in vertical, horizontal and longitudinal directions increases with the increase of the ratio of the low-frequency energy to the total energy; (2) it is the largest when the surge is dominant, the second largest when the wind waves and surge are equal, and the smallest when the wind waves are dominant; (3) the motion amplitude of both hulls in the double-peak spectral waves is greater than that of the single-peak spectral wind waves under the premise that the total energy is the same, and (4) the motion amplitude of both hulls in the double-peak spectral waves is greater than that of the single-peak spectral wind waves. The study shows that the influence of double-peak spectral waves should be considered in the mooring design and safety planning of FPSO operation system.

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我国南海海域受西太平洋热带气旋和台风影响，易出现双峰甚至多峰的混合浪形式波浪，对海洋浮式结构物的作业安全形成潜在危害。为此本文基于势流理论，同时考虑不同装载状态的影响，对FPSO与穿梭油轮旁靠系统在双峰谱波浪、单峰谱波浪状态下的运动响应展开对比研究。分别计算两船体在风浪为主、风涌相当及涌浪为主的双峰谱波浪状态下和单峰谱风浪状态下运动响应。计算结果表明：两船体在垂荡、横摇和纵摇方向上的运动幅值随低频能量占总能量比例的增加而增加，涌浪为主时最大，风涌相当时次之，风浪为主时最小，在总能量相同的前提下，双峰谱波浪状态下两船体运动幅值均大于单峰谱风浪状态下的运动幅值。研究表明，在FPSO作业系统的系泊设计和安全生产规划中，需对双峰谱波浪的影响予以考虑。

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通讯作者，E-mail：
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郭汶灵（2000-），男，硕士

王许洁（1982-），男，博士，副教授，通讯作者，E-mail：。

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郭汶灵（2000-），男，硕士

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王许洁（1982-），男，博士，副教授，通讯作者，E-mail：。

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王许洁（1982-），男，博士，副教授，通讯作者，E-mail：。

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journalId=1240685776644648972, articleId=1243896355505161147, language=CN, label=图8, caption=FPSO及穿梭油轮纵摇运动幅值, figureFileSmall=Gnjh3NOxeSloCMKEdYDxiw==, figureFileBig=kT8ewVgCDzLaiotOx+2nIA==, tableContent=null), ArticleFig(id=1243896368364896648, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896355505161147, language=EN, label=Tab.1, caption=

Main parameters of FPSO

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设计参数总长/m型宽/m型深/m吃水/m排水量/t
压载20736165.731 126
半载20736168.749 444
满载20736161297 771
), ArticleFig(id=1243896368511697294, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896355505161147, language=CN, label=表1, caption=

FPSO主要参数

, figureFileSmall=null, figureFileBig=null, tableContent=
设计参数总长/m型宽/m型深/m吃水/m排水量/t
压载20736165.731 126
半载20736168.749 444
满载20736161297 771
), ArticleFig(id=1243896368620749203, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896355505161147, language=EN, label=Tab.2, caption=

Main parameters of shuttle tanker

, figureFileSmall=null, figureFileBig=null, tableContent=
设计参数总长/m型宽/m型深/m吃水/m排水量/t
压载235.64624.116151 505.8
半载2354624.111104 748.4
满载235.64624.18.577 766.1
), ArticleFig(id=1243896368717218202, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896355505161147, language=CN, label=表2, caption=

穿梭油轮主要参数

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设计参数总长/m型宽/m型深/m吃水/m排水量/t
压载235.64624.116151 505.8
半载2354624.111104 748.4
满载235.64624.18.577 766.1
), ArticleFig(id=1243896368880796062, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896355505161147, language=EN, label=Tab.3, caption=

Wave calculation conditions

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波浪类型波浪谱有效波高/m谱峰周期/s
风浪JONSWAP谱2.54.5
涌浪JONSWAP谱2.5810121416
风浪为主双峰谱波浪Ochi-Hubble谱高频部分2.2364.5
低频部分1.118810121416
风涌相当双峰谱波浪Ochi-Hubble谱高频部分1.7684.5
低频部分1.768810121416
涌浪为主双峰谱波浪Ochi-Hubble谱高频部分1.1184.5
低频部分2.236810121416
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波浪计算工况

, figureFileSmall=null, figureFileBig=null, tableContent=
波浪类型波浪谱有效波高/m谱峰周期/s
风浪JONSWAP谱2.54.5
涌浪JONSWAP谱2.5810121416
风浪为主双峰谱波浪Ochi-Hubble谱高频部分2.2364.5
低频部分1.118810121416
风涌相当双峰谱波浪Ochi-Hubble谱高频部分1.7684.5
低频部分1.768810121416
涌浪为主双峰谱波浪Ochi-Hubble谱高频部分1.1184.5
低频部分2.236810121416
), ArticleFig(id=1243896369061151140, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896355505161147, language=EN, label=Tab.4, caption=

Specific parameters of multi-point mooring and side-by-side connecting system

, figureFileSmall=null, figureFileBig=null, tableContent=
名称长度/m直径/m湿重/（kg·m−1）破断强度/N刚度/N
船链2000.1473801.900E71.627E9
钢缆3000.12879.51.589E71.505E9
旁靠缆—0.12—1.03E73.18E8
护舷—4——1.786E6
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多点系泊及旁靠系统具体参数

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名称长度/m直径/m湿重/（kg·m−1）破断强度/N刚度/N
船链2000.1473801.900E71.627E9
钢缆3000.12879.51.589E71.505E9
旁靠缆—0.12—1.03E73.18E8
护舷—4——1.786E6
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Surface elements number of hull wet surface

, figureFileSmall=null, figureFileBig=null, tableContent=
船体FPSO满载-穿梭油轮压载面元数FPSO半载-穿梭油轮半载面元数FPSO压载-穿梭油轮满载面元数
FPSO11 78199138950
穿梭油轮510063017283
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船体湿表面面元数

, figureFileSmall=null, figureFileBig=null, tableContent=
船体FPSO满载-穿梭油轮压载面元数FPSO半载-穿梭油轮半载面元数FPSO压载-穿梭油轮满载面元数
FPSO11 78199138950
穿梭油轮510063017283
), ArticleFig(id=1243896369723851197, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896355505161147, language=EN, label=Tab.6, caption=

Comparison of 6-DOF motion responses of FPSO

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垂荡/m横摇/（°）纵摇/（°）
水池实验数据最大值0.320.610.48
最小值−0.50−0.64−0.47
数值模拟数据最大值0.770.410.56
最小值−0.88−0.70−0.52
), ArticleFig(id=1243896369845486020, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896355505161147, language=CN, label=表6, caption=

FPSO六自由度运动量对比

, figureFileSmall=null, figureFileBig=null, tableContent=
垂荡/m横摇/（°）纵摇/（°）
水池实验数据最大值0.320.610.48
最小值−0.50−0.64−0.47
数值模拟数据最大值0.770.410.56
最小值−0.88−0.70−0.52
), ArticleFig(id=1243896369983898057, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896355505161147, language=EN, label=Tab.7, caption=

Statistical values of motion amplitude of FPSO and shuttle tanker

, figureFileSmall=null, figureFileBig=null, tableContent=
压载状态波浪类型运动幅值
垂荡/m横摇/（°）纵摇/（°）
FPSO穿梭油轮FPSO穿梭油轮FPSO穿梭油轮
FPSO满载、穿梭油轮压载单风浪0.2030.1380.0440.1520.0260.058
风浪为主2.4233.6080.1660.5571.1371.629
风涌相当4.3936.5570.2720.8442.1472.598
涌浪为主5.4288.3960.4001.2272.5603.792
FPSO压载、穿梭油轮满载单风浪0.2310.4500.1960.5670.0320.036
风浪为主2.5032.9770.7901.0591.1931.369
风涌相当4.5975.3511.0431.4782.2482.643
涌浪为主5.8836.7121.5362.2132.7633.242
), ArticleFig(id=1243896370109727185, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896355505161147, language=CN, label=表7, caption=

FPSO及穿梭油轮运动幅值统计

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压载状态波浪类型运动幅值
垂荡/m横摇/（°）纵摇/（°）
FPSO穿梭油轮FPSO穿梭油轮FPSO穿梭油轮
FPSO满载、穿梭油轮压载单风浪0.2030.1380.0440.1520.0260.058
风浪为主2.4233.6080.1660.5571.1371.629
风涌相当4.3936.5570.2720.8442.1472.598
涌浪为主5.4288.3960.4001.2272.5603.792
FPSO压载、穿梭油轮满载单风浪0.2310.4500.1960.5670.0320.036
风浪为主2.5032.9770.7901.0591.1931.369
风涌相当4.5975.3511.0431.4782.2482.643
涌浪为主5.8836.7121.5362.2132.7633.242
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FPSO旁靠系统在双峰谱波浪下的运动响应研究
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郭汶灵 1 , 王许洁 1 , 田哲 1 , 熊冶平 2
船舶力学 | 流体力学 2025,29(9): 1397-1406
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船舶力学 | 流体力学 2025, 29(9): 1397-1406
FPSO旁靠系统在双峰谱波浪下的运动响应研究
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郭汶灵1, 王许洁1 , 田哲1, 熊冶平2
作者信息
  • 1.中国海洋大学　工程学院，山东　青岛　266000
  • 2.南安普顿大学　工程与物理学系，英国　南安普顿　SO167QF

    • 郭汶灵（2000-），男，硕士

    王许洁（1982-），男，博士，副教授，通讯作者，E-mail：。

通讯作者:

通讯作者，E-mail：
Motion response of FPSO system under bimodal spectrum waves
Wen-ling GUO1, Xu-jie WANG1 , Zhe TIAN1, Ye-ping XIONG2
Affiliations
  • 1.College of Engineering, Ocean University of China, Qingdao 266000, China
  • 2.Faculty of Engineering and Physical Sciences, University of Southampton, Southampton SO167QF, UK
出版时间: 2025-09-20 doi: 10.3969/j.issn.1007-7294.2025.09.006
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摘要
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我国南海海域受西太平洋热带气旋和台风影响，易出现双峰甚至多峰的混合浪形式波浪，对海洋浮式结构物的作业安全形成潜在危害。为此本文基于势流理论，同时考虑不同装载状态的影响，对FPSO与穿梭油轮旁靠系统在双峰谱波浪、单峰谱波浪状态下的运动响应展开对比研究。分别计算两船体在风浪为主、风涌相当及涌浪为主的双峰谱波浪状态下和单峰谱风浪状态下运动响应。计算结果表明：两船体在垂荡、横摇和纵摇方向上的运动幅值随低频能量占总能量比例的增加而增加，涌浪为主时最大，风涌相当时次之，风浪为主时最小，在总能量相同的前提下，双峰谱波浪状态下两船体运动幅值均大于单峰谱风浪状态下的运动幅值。研究表明，在FPSO作业系统的系泊设计和安全生产规划中，需对双峰谱波浪的影响予以考虑。

FPSO旁靠系统  /  双峰谱波浪  /  运动响应  /  多点系泊

The South sea of China is affected by tropical cyclones and typhoons in the western Pacific Ocean, which are prone to double-peak or even multi-peak waves in the form of mixed waves, which are potentially hazardous to the operational safety of marine floating structures. Therefore, based on the potential flow theory and considering the influence of different loading states, a comparative study was conducted on the motion response of FPSO and shuttle tanker side-by-side system under double-peak spectral wave and single-peak spectral wave states. The motion responses of the two hulls in the double-peak spectral wave states of mainly wind waves, wind waves and surge are equal, and mainly surge and the single-peak spectral wind waves state are calculated respectively. The calculation results show that (1) the amplitude of the motion of the two hulls in vertical, horizontal and longitudinal directions increases with the increase of the ratio of the low-frequency energy to the total energy; (2) it is the largest when the surge is dominant, the second largest when the wind waves and surge are equal, and the smallest when the wind waves are dominant; (3) the motion amplitude of both hulls in the double-peak spectral waves is greater than that of the single-peak spectral wind waves under the premise that the total energy is the same, and (4) the motion amplitude of both hulls in the double-peak spectral waves is greater than that of the single-peak spectral wind waves. The study shows that the influence of double-peak spectral waves should be considered in the mooring design and safety planning of FPSO operation system.

side-by-side system of FPSO  /  double-peak spectral waves  /  motion response  /  multi-point mooring
郭汶灵, 王许洁, 田哲, 熊冶平. FPSO旁靠系统在双峰谱波浪下的运动响应研究. 船舶力学, 2025 , 29 (9) : 1397 -1406 . DOI: 10.3969/j.issn.1007-7294.2025.09.006
Wen-ling GUO, Xu-jie WANG, Zhe TIAN, Ye-ping XIONG. Motion response of FPSO system under bimodal spectrum waves[J]. Journal of Ship Mechanics, 2025 , 29 (9) : 1397 -1406 . DOI: 10.3969/j.issn.1007-7294.2025.09.006
正文
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0　引言
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浮式生产储油船（FPSO）目前被广泛应用于海上石油生产和储存领域[1]，因采用海底管路将原油外输至陆地成本过高，海上原油外输的主要方式是利用穿梭油轮将经FPSO预处理后的原油运送至陆地。外输方式可分为串靠卸载和旁靠卸载[2]，根据穿梭油轮相对于FPSO的靠泊位置定义串靠或旁靠，串靠卸载方式即采用FPSO与穿梭油轮一前一后的串列式靠泊方式，旁靠卸载通常指穿梭油轮靠泊于FPSO左舷，两船之间旁靠距离为4~10 m。对于有效波高小于2.5 m相对温和的海况，旁靠卸载所需系泊设施和原油运输软管更少，是一种更加经济可行的卸载方式[3]。
目前国内外针对FPSO旁靠外输开展了多浮体的水动力性能研究。周珂等[4]结合理论分析和模型实验，研究了实际海洋环境中斜浪对多浮体水动力性能的影响；王文华等[5]基于频域波浪势流理论讨论了旁靠外输系统单浮体水动力特性和双浮体的耦合作用；Zhao等[6]采用三种典型的不规则波环境工况，得到了旁靠卸载过程双船之间的相对运动与连接系统所受载荷之间的关系；Xu等[7]从频域和时域两方面全面研究了FPSO和穿梭油轮在旁靠卸载过程中对水动力特性的耦合效应；Yue等[8]分析了旁靠系泊卸载系统在风、浪、流耦合作用下，对旁靠卸载作业安全影响较大的两船间垂荡、横摇和纵摇自由度的相对运动幅值。
实际海况中大部分波浪以混合浪形式出现[9]，混合浪波浪谱一般呈现双峰甚至多峰。DNV规范[10]建议，设计过程中在计算大型海洋工程结构物所受的波浪荷载时，应当考虑双峰谱波浪。
本文对FPSO与穿梭油轮旁靠系统在双峰谱波浪、单峰谱波浪状态下的运动响应展开对比研究，所设定风、浪、流入射方向均为180°。考虑到船体的对称性，主要对安全性能影响最大的垂荡、横摇和纵摇三自由度运动响应进行计算分析[8]。首先，基于三维势流理论，对各船舶水动力性能和系泊系统的安全性进行了计算校核[11-12]；然后，针对不同类型双峰谱混合浪状态，对旁靠外输作业状态下两船的垂荡、横摇和纵摇自由度的时域运动响应展开研究；最后，探讨在总能量相同状态下，双峰谱混合浪相对于单峰谱波浪对原油卸载作业的危害程度。本文研究可为旁靠卸载方案设计和安全生产提供一定的设计参考。
1　FPSO及穿梭油轮旁靠系统
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1.1　研究对象
本文以一艘作业于中国南海东部海域的FPSO为研究对象，FPSO主要参数见表1，穿梭油轮主要参数见表2。
1.2　环境参数
根据高低频能量在双峰谱波浪中所占能量比例不同，本文选用风浪为主（高频能量占主导成分）、风涌相当（高、低频能量均等）、涌浪为主（低频能量占主导成分）三种不同类型的双峰谱波浪[13]。为对比分析双峰谱波浪状态下的运动响应结果与单峰谱波浪状态下的差异，试验过程中采用JONSWAP谱模拟单峰谱波浪，双峰谱波浪频谱采用Ochi-Hubble六参数谱[14]，其特征参数包含有效波高、谱峰周期及形状参数，由低频和高频两部分的特征参数共同组成。试验过程中令双峰谱波浪与单峰谱波浪总能量相同，有效波高均设定为2.5 m，调整双峰谱形状参数λ与单峰谱的谱峰升高因子γ=3.3保持一致。由于低频长周期波浪通常对海洋浮式结构物产生更为不利的影响[15]，固定高频风浪的谱峰周期为4.5 s不变，而低频谱峰周期在8~16 s范围内变化，具体见表3。
为更好地模拟旁靠外输过程的实际作业环境，本文拟采用NPD谱模拟作业海域实际风况，取海面以上高度10 m处的平均风速为13 m/s；海流采用表层流速进行模拟，设定自由表面附近的流速为0.55 m/s。风、浪、流在本文中入射方向均设定为180°，即船舶迎浪方向。
1.3　系泊系统
本文研究对象FPSO作业于200 m水深的南海海域，采用多点系泊系统进行定位，系泊系统由12根系泊缆组成，每三根系泊缆为一组，系泊缆相对于FPSO船体的中纵剖面呈对称布置，同组三根系泊缆之间的夹角为5°，系泊缆自上（导缆孔）而下（海底锚）选用船链+钢缆+船链的组合形式，图1所示为多点系泊系统示意图。
FPSO与穿梭油轮两船体间通过由10根旁靠缆和6个橡胶材质护舷所组成的旁靠系统连接，该连接方式可最大程度避免旁靠作业过程中发生碰撞或脱离。旁靠缆与护舷具体布置见图2。系泊缆各段具体参数、旁靠缆参数以及护舷参数见表4。
2　数值计算理论
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海洋结构物以自由面为基准时，速度势满足如下Laplace方程：
Laplace方程和描述物体运动的速度势都需要进行线性化处理。流体中流体总的速度势定义为
总速度势是由入射波、辐射波和绕射波叠加而成[16]，因此总速度势可以分解为
式中，ϕI为入射波速度式，表明流场中速度分布的情况；ϕD为绕射势，表明结构物对流场内的速度产生的影响；ϕR为辐射势，表明结构物6个自由度的运动及振荡对流场的影响；ω为入射波的频率。
船舶在规则波作用下的运动微分方程为
式中，Ms为结构质量矩阵，Ma为水动力附加质量矩阵，C为系统线性阻尼矩阵，Ks为系统总刚度矩阵，F为系统所受的波浪力，X为幅值响应算子（RAOs），ω为入射波的频率。
3　时域分析
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3.1　计算模型
两船体三维模型采用实尺度进行建模，图3为FPSO与穿梭油轮面元模型，采用AQWA进行分析计算时，由于网格划分尺寸越小，能够模拟的波浪频率越高，但网格划分尺寸过小会影响计算速度，在考虑波浪谱能量范围、计算机计算速度和模型精度的因素下，网格单元边长尺寸取为2 m[17]，由网格单元尺寸决定的波浪频率范围为0.1~2.50 rad/s，对于本文计算海域南海的海浪谱频率而言，该频率范围已能够涵盖大部分能量，符合计算要求。由于FPSO与穿梭油轮在旁靠外输作业时不同装载状态的吃水深度会发生实时变化，进行网格划分时面元模型湿表面面元数也将随之发生变化，各装载状态下湿面元数统计见表5。本文采用在两船体间的自由液面上设置阻尼盖的方式以抑制驻波现象，使间隙自由液面运动更加接近真实工况，降低间隙共振效应带来的数据误差，阻尼系数取值为0.2。
3.2　数值仿真计算验证
为验证本文数值仿真计算的准确性，将其与章柯等[18]在江苏科技大学综合水池进行的不规则波试验结果进行对比，数值计算采用相同的实验环境和模型，时域计算时长为3小时，通过JONSWAP谱模拟不规则波海浪，特征参数依照真实海况环境具体设定如下：有效波高为2.5 m，谱峰周期为10 s，谱峰升高因子为3。由于横荡、纵荡和艏摇自由度上的运动具有低频特性，需要进行长时间的波浪实验，短时间的水池实验结果存在较大误差[19]，因此仅对后续计算分析所需的垂荡、横摇和纵摇三个自由度的运动响应结果进行对比，结果见表6。
通过结果对比可知，在这三个自由度上的运动具有波频特性，实验结果与模拟结果吻合程度较好，本文采用数值仿真分析研究旁靠外输系统在垂荡、横摇和纵摇自由度的时域运动响应能够满足计算要求。
3.3　时域分析结果
3.3.1　缆绳张力分析
利用AQWA软件，开展FPSO与穿梭油轮组成的旁靠外输系统三小时内的时域运动响应分析，通过时域分析结果对比FPSO及穿梭油轮在三种不同类型双峰谱波浪状态下的运动幅值可知，涌浪为主的双峰谱波浪对旁靠外输作业的危害性更为显著，因此本小节以涌浪为主的双峰谱波浪作为环境工况，开展数据统计分析以验证系泊系统设计布置的合理性。
系泊系统采用悬链式多点系泊，系泊缆预张力设定为系泊缆最大破断强度的10%。图4为不同谱峰周期的双峰谱波浪状态下FPSO 1#~12#系泊缆的张力值。结果表明，三种装载状态下4#~9#系泊缆均大于系泊于船尾部位的其余缆绳。在FPSO满载、穿梭油轮压载情况下，系泊缆最大张力值随谱峰周期的增大而减小，其余两种装载状态下，4#~6#系泊缆张力随谱峰周期的增大呈减小趋势，7#~9#系泊缆张力在谱峰周期12 s附近达到最大值，其最大张力值随谱峰周期的增长呈现先增大后减小的趋势。三种装载状态下的安全系数分别为9.45、7.66及6.72，均满足设计规范要求。
图5为不同低频谱峰周期涌浪为主的双峰谱波浪状态下连接FPSO及穿梭油轮的旁靠缆张力值，选取H1和H10作为研究对象。可知，在FPSO满载、穿梭油轮压载情况下，H1和H10的最大张力值均随谱峰周期的增加而减小；其余两种状态下，旁靠缆最大张力值随谱峰周期的增长，呈现先增加后减小趋势，并在谱峰周期12 s附近达到最大值。三种装载状态下安全系数分别为3.43、2.23及2.36，均满足设计规范要求。
3.3.2　运动响应分析
由于旁靠外输作业过程中两船体在垂荡、横摇及纵摇方向上的运动响应对作业安全影响较大，本小节时域分析重点针对FPSO及穿梭油轮在该三个方向上的运动响应幅值进行统计分析，FPSO半载、穿梭油轮半载的两船体在不同谱峰周期的双峰谱波浪状态下，垂荡、横摇和纵摇方向上的运动幅值结果分析分别见图6-8。
从图6可知，对于垂荡运动幅值，随低频谱峰周期增大，垂荡幅值逐渐增大，且运动幅值与低频能量占总能量的比重呈正相关，即两船体在涌浪为主的双峰谱波浪状态下的垂荡幅值最为显著，且与其他类型波浪差异明显。最大值出现在低频谱峰周期16 s时，两船体垂荡幅值分别为5.591 m和6.865 m，约为风浪状态下垂荡幅值的26.49倍和21.45倍。
从图7可知，对于横摇运动幅值，随着低频谱峰周期的增大，横摇幅值在8~16 s范围内呈现先增加后减少趋势，在低频谱峰周期12 s时，横摇幅值达到最大值，其原因是谱峰周期在此时接近船体固有周期，导致两船体运动响应更加剧烈。FPSO与穿梭油轮的横摇幅值分别为1.42°和3.77°，约为风浪状态下横摇幅值的9.47倍和9.49倍。
从图8可知，纵摇运动幅值的变化规律与垂荡幅值随谱峰周期的变化规律相似，纵摇幅值随低频谱峰周期的增长而增加，在低频谱峰周期12 s之后，穿梭油轮纵摇幅值的增长趋势有所放缓。在低频谱峰周期16 s时，不同类型波浪状态下的两船体纵摇幅值的差异最为显著，FPSO与穿梭油轮纵摇幅值最大值分别为2.7°和3.327°，约为风浪状态下纵摇幅值的87.09倍和48.22倍。
针对其余两种装载状态下两船体的运动响应结果分析，统计其在垂荡、横摇和纵摇三个方向上的运动幅值在波浪周期8~16 s范围内的最大值，以便直观对比双峰谱波浪相比单峰谱波浪对于旁靠卸载作业的危害性，统计结果见表7。
从表中可知，FPSO及穿梭油轮在三个方向上运动幅值的最大值出现在以涌浪为主的双峰谱波浪状态下，垂荡幅值最大值分别为5.883 m和8.396 m，约为风浪状态下的26.74倍和60.84倍；横摇幅值最大值分别为1.536°和2.213°，约为风浪状态下的9.09倍和8.07倍；纵摇幅值最大值分别为2.763°和3.792°，约为风浪状态下的98.46倍和90.06倍；同FPSO半载、穿梭油轮半载状态具有相似规律，两船体运动幅值均随低频能量占总能量比重的增加而增加。对比不同装载阶段FPSO及穿梭油轮在涌浪为主双峰谱波浪状态下的运动幅值可知，FPSO满载、穿梭油轮压载状态时，穿梭油轮的垂荡和纵摇幅值均大于其余装载阶段的运动幅值，最大值分别为8.396 m和3.792°。FPSO压载、穿梭油轮满载状态时，FPSO的垂荡、横摇及纵摇幅值均大于其余装载阶段的运动幅值，最大值分别为5.883 m、1.536°和2.763°。垂荡和纵摇幅值最大值均出现在两船体分别处于压载状态时，运动幅值随原油装载量的减小而增大。因此，在实际进行旁靠外输作业过程中，应重点关注低频谱峰周期接近船舶固有周期的以涌浪为主的双峰谱波浪，同时尽量缩短旁靠外输前期和后期作业时间，以确保旁靠外输作业的安全。
4　结论
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本文通过数值模拟方法研究了三种不同类型双峰谱波浪对FPSO旁靠系统的运动响应，对比分析了与之总能量相同的单峰谱风浪状态下的运动响应差异。主要结论如下：
（1）对于进行旁靠外输作业的FPSO与穿梭油轮，垂荡、横摇和纵摇幅值随低频能量占总能量比重的增大而增大，涌浪为主时最大，风涌相当时次之，风浪为主时最小；在总能量相同时，两船体在三种不同类型的双峰谱波浪状态下的垂荡、横摇和纵摇幅值均大于风浪状态下的运动幅值。因此，在实际原油外输作业中，应对作业海域涌浪为主的双峰谱波浪重点关注。
（2）对比三种装载状态FPSO与穿梭油轮在涌浪为主的双峰谱波浪状态下的运动幅值，发现两船体均处于压载状态时其垂荡和纵摇运动幅值最大，且运动幅值随原油装载量的减小而增大。因此，在旁靠卸载作业过程中FPSO满载、穿梭油轮压载和FPSO压载、穿梭油轮满载两种装载状态下的原油输送时间应尽量缩短。
（3）在低频谱峰周期为12 s时，系泊缆张力和旁靠缆张力均达到最大值，旁靠缆张力随低频谱峰周期增加的变化最为显著，最大可达低频谱峰周期8 s时的3.89倍。因此，在进行原油旁靠外输作业时，应重点关注低频谱峰周期接近船舶固有周期的双峰谱波浪。
基金
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  • 国家留学基金资助项目(202406330126)
  • 国家自然科学基金资助项目(52271296; 51709246)
  • 山东高校青年创新团队项目(2023KJ036)
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2025年第29卷第9期
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doi: 10.3969/j.issn.1007-7294.2025.09.006
  • 接收时间：2025-03-14
  • 首发时间：2026-03-26
  • 出版时间：2025-09-20
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  • 收稿日期：2025-03-14
基金
国家留学基金资助项目(202406330126)
国家自然科学基金资助项目(52271296; 51709246)
山东高校青年创新团队项目(2023KJ036)
作者信息
    1.中国海洋大学　工程学院，山东　青岛　266000
    2.南安普顿大学　工程与物理学系，英国　南安普顿　SO167QF

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