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Article(id=1210590158446007116, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1210590152548807015, articleNumber=null, orderNo=null, doi=10.16790/j.cnki.1009-9239.im.2024.09.012, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1697472000000, receivedDateStr=2023-10-17, revisedDate=1702656000000, revisedDateStr=2023-12-16, acceptedDate=null, acceptedDateStr=null, onlineDate=1766556785451, onlineDateStr=2025-12-24, pubDate=1726761600000, pubDateStr=2024-09-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1766556785451, onlineIssueDateStr=2025-12-24, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1766556785451, creator=13701087609, updateTime=1766556785451, updator=13701087609, issue=Issue{id=1210590152548807015, tenantId=1146029695717560320, journalId=1149653034449285133, year='2024', volume='57', issue='9', pageStart='1', pageEnd='165', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1766556784044, creator=13701087609, updateTime=1766563998200, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1210620410958312217, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1210590152548807015, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1210620410958312218, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1210590152548807015, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=114, endPage=124, ext={EN=ArticleExt(id=1210590159687521123, articleId=1210590158446007116, tenantId=1146029695717560320, journalId=1149653034449285133, language=EN, title=Study on temperature field and ampacity calculation of umbilical cable under coupling of electro-thermal-fluid multi-physical fields, columnId=1192878364340924664, journalTitle=Insulating Materials, columnName=Test and Analysis, runingTitle=null, highlight=null, articleAbstract=

Umbilical cables are known as the "nerve lifeline" connecting underwater production systems and upper facilities, and accurate analysis of their temperature field distribution and ampacity is a key guarantee for safe offshore oil and gas exploration and production tasks. Unlike traditional submarine cables, umbilical cables have complex electro-thermal-fluid multi-physical fields coupling effects due to their complex structure and diverse functions, and it is difficult to determine their temperature field distribution and ampacity by traditional analytical methods. A fine cross-sectional model of multi-field coupling of umbilical cable was established based on the finite element software COMSOL in this paper, and the influence of three typical laying methods, environment and other factors on the conductor temperature and steady-state ampacity was studied by the control variable method. The results show that when the current is small, the temperature of the fluid in tube is the dominant factor affecting the cross-sectional temperature and steady-state ampacity of umbilical cable. The trend of conductor temperature can reflect the change of steady-state ampacity. When buried directly, the increase of buried depth and the external fluid temperature will weaken the heat dissipation capacity of umbilical cable. When tiled, the seawater flow significantly reduces the temperature of umbilical cable, and at low flow rates, the increase of flow rate has a significant cooling effect on the umbilical cable. However, the high flow rate of seawater will form a boundary layer with temperature gradient on the surface close to the umbilical cable, making the heat transfer be restricted, and the cooling effect is not obvious. The insulation ageing has less influence on the overall temperature distribution of umbilical cable, but it affects the maximum temperature of the cross-section.

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脐带缆被誉为连接水下生产系统和上部设施的“神经生命线”，准确分析其温度场分布和载流量是安全开展海洋油气勘探和开采任务的关键保障。不同于传统海缆，脐带缆因结构复杂、功能多样，在位运行时存在复杂的电-热-流多物理场耦合效应，传统解析法难以确定其温度场分布和载流量。本文基于有限元软件Comsol建立脐带缆电-热-流多物理场耦合截面精细模型，通过控制变量法研究3种典型敷设方式、环境等因素对导体温度和稳态载流量的影响。结果表明：当电流较小时，影响脐带缆截面温度和稳态载流量的主导因素是管中液体温度；导体温度的变化趋势能够反映稳态载流量的变化情况；直埋时，埋设深度与外界流体温度的增加皆会削弱脐带缆的散热能力；平铺时，海水流动会明显降低脐带缆温度，在低流速下，流速增加对脐带缆的降温效果十分显著，但高流速的海水会在紧贴脐带缆的表面形成具有温度梯度的边界层，使热量的传递受到限制，降温效果反而不明显；绝缘老化对脐带缆整体温度分布的影响较小，但会影响截面最高温度。

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娄敏（1981-），女（汉族），山东曲阜人，教授，博士，主要深水新型立管力学分析与优化设计、海洋管道流固耦合及振动抑制、深水柔性管道设计与研发研究。
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范昌泓（1999-），男（汉族），福建大田人，硕士生，主要从事脐带缆多物理场耦合分析。

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范昌泓（1999-），男（汉族），福建大田人，硕士生，主要从事脐带缆多物理场耦合分析。

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范昌泓（1999-），男（汉族），福建大田人，硕士生，主要从事脐带缆多物理场耦合分析。

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Xuzhou: China University of Mining and Technology,2023., articleTitle=Study of temperature distribution characteristics of cables based on thermal circuit model and fiber optic temperature sensing principle, refAbstract=null)], funds=[Fund(id=1218262753240858763, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, awardId=U2006226, language=CN, fundingSource=国家自然科学联合基金重点项目资助(U2006226), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1218262747440136978, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, xref=null, ext=[AuthorCompanyExt(id=1218262747448525588, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, companyId=1218262747440136978, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, China), 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journalId=1149653034449285133, articleId=1210590158446007116, language=EN, label=Fig.2, caption=Schematic diagram of umbilical cable laying method, figureFileSmall=bNq/MZ9DHoSF1rK8SRkU9g==, figureFileBig=fZlouCy+QWTZFjPBbThxCg==, tableContent=null), ArticleFig(id=1218262750099325881, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=CN, label=图2, caption=脐带缆敷设方式示意图, figureFileSmall=bNq/MZ9DHoSF1rK8SRkU9g==, figureFileBig=fZlouCy+QWTZFjPBbThxCg==, tableContent=null), ArticleFig(id=1218262750258709440, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=EN, label=Fig.3, caption=Steady-state equivalent thermal circuit model of umbilical cable, figureFileSmall=Fn8ECnlKN+DP9VscVyJBXg==, figureFileBig=hqnuVN5ZtiLjfzG1y5Bu0A==, tableContent=null), ArticleFig(id=1218262750363567051, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=CN, label=图3, caption=脐带缆稳态等效热路模型, figureFileSmall=Fn8ECnlKN+DP9VscVyJBXg==, figureFileBig=hqnuVN5ZtiLjfzG1y5Bu0A==, tableContent=null), ArticleFig(id=1218262750506173393, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=EN, label=Fig.4, caption=Variation curves of umbilical cable section temperature with current, figureFileSmall=jNvsYdjz09nh6Y9kgyoLag==, figureFileBig=4qYpK4G/sRCJSp64fDy2cw==, tableContent=null), ArticleFig(id=1218262750598448087, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=CN, label=图4, caption=脐带缆截面温度随电流的变化曲线, figureFileSmall=jNvsYdjz09nh6Y9kgyoLag==, figureFileBig=4qYpK4G/sRCJSp64fDy2cw==, tableContent=null), ArticleFig(id=1218262750682334176, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=EN, label=Fig.5, caption=Steady-state temperature distribution of XLPE insulation at different current, figureFileSmall=veOBug7XNaSyyftCWy3lCA==, figureFileBig=c252iVrB22tt55u+L9n2LQ==, tableContent=null), ArticleFig(id=1218262750782997480, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=CN, label=图5, caption=不同电流下的XLPE绝缘温度分布, figureFileSmall=veOBug7XNaSyyftCWy3lCA==, figureFileBig=c252iVrB22tt55u+L9n2LQ==, tableContent=null), ArticleFig(id=1218262750883660782, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=EN, label=Fig.6, caption=Conductor temperature and steady-state ampacity of umbilical cables at different burial depths, figureFileSmall=e4JPNhl/CXNohQdNqaCkrQ==, figureFileBig=23s+10W7EU/kIQwTM9/hAg==, tableContent=null), ArticleFig(id=1218262750992712696, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=CN, label=图6, caption=不同埋设深度下脐带缆的导体温度与稳态载流量, figureFileSmall=e4JPNhl/CXNohQdNqaCkrQ==, figureFileBig=23s+10W7EU/kIQwTM9/hAg==, tableContent=null), ArticleFig(id=1218262751055627262, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=EN, label=Fig.7, caption=Conductor temperature and conductor conductivity of umbilical cables at different burial depths, figureFileSmall=KcPoWuSxJBJ6UjBgU3IJfg==, figureFileBig=oEodCQtl2hMV60/osrzwCg==, tableContent=null), ArticleFig(id=1218262751126929409, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=CN, label=图7, caption=不同埋设深度下脐带缆的导体温度与导体电导率, figureFileSmall=KcPoWuSxJBJ6UjBgU3IJfg==, figureFileBig=oEodCQtl2hMV60/osrzwCg==, tableContent=null), ArticleFig(id=1218262751223398408, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=EN, label=Fig.8, caption=Conductor temperature under different flow rates and seawater temperatures, figureFileSmall=urjoE6hUBpG7a1ohAEutkg==, figureFileBig=G6lrHMlj/KfUqDJSTvms+w==, tableContent=null), ArticleFig(id=1218262751315673104, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=CN, label=图8, caption=不同海水流速和温度下导体温度, figureFileSmall=urjoE6hUBpG7a1ohAEutkg==, figureFileBig=G6lrHMlj/KfUqDJSTvms+w==, tableContent=null), ArticleFig(id=1218262751445696536, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=EN, label=Fig.9, caption=Conductor temperature curves under different seawater temperatures, figureFileSmall=nOjlmpAc29YdewcHN6EJzw==, figureFileBig=lAxONSv5ZAGm57DJjbaO1w==, tableContent=null), ArticleFig(id=1218262751554748449, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=CN, label=图9, caption=不同海水温度下导体温度变化曲线, figureFileSmall=nOjlmpAc29YdewcHN6EJzw==, figureFileBig=lAxONSv5ZAGm57DJjbaO1w==, tableContent=null), ArticleFig(id=1218262751638634536, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=EN, label=Fig.10, caption=Temperature distribution of umbilical cables with different degrees of insulation ageing, figureFileSmall=gQTxwpVWoEHOtYgwrKVApg==, figureFileBig=TXGHfZZnoBb5XNWeCAnSwA==, tableContent=null), ArticleFig(id=1218262751722520619, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=CN, label=图10, caption=不同绝缘老化程度下脐带缆的温度分布图, figureFileSmall=gQTxwpVWoEHOtYgwrKVApg==, figureFileBig=TXGHfZZnoBb5XNWeCAnSwA==, tableContent=null), ArticleFig(id=1218262751835766838, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=EN, label=Table 1, caption=Structure parameters of umbilical cable, figureFileSmall=null, figureFileBig=null, tableContent=
结构名称厚度/mm外径/mm
电缆单元阻水铜导体—35.28
导体屏蔽1.638.48
XLPE绝缘6.852.08
绝缘屏蔽1.655.28
铅护套2.259.68
电缆护套4.668.80
包带2.0152.24
管单元不锈钢管1.546.00
管单元护套2.050.00
光纤单元光纤—10.00
不锈钢管2.014.00
光纤护套18.050.00
填充单元小填充绳—10.64/16.00
大填充绳—32.34/50.00
铠装单元镀锌钢丝—9.12
护套单元内护套4.6261.36
外护套9.1316.08
), ArticleFig(id=1218262751928041533, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=CN, label=表1, caption=

脐带缆结构参数

, figureFileSmall=null, figureFileBig=null, tableContent=
结构名称厚度/mm外径/mm
电缆单元阻水铜导体—35.28
导体屏蔽1.638.48
XLPE绝缘6.852.08
绝缘屏蔽1.655.28
铅护套2.259.68
电缆护套4.668.80
包带2.0152.24
管单元不锈钢管1.546.00
管单元护套2.050.00
光纤单元光纤—10.00
不锈钢管2.014.00
光纤护套18.050.00
填充单元小填充绳—10.64/16.00
大填充绳—32.34/50.00
铠装单元镀锌钢丝—9.12
护套单元内护套4.6261.36
外护套9.1316.08
), ArticleFig(id=1218262752070647875, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=EN, label=Table 2, caption=Conductivity of materials in umbilical cable, figureFileSmall=null, figureFileBig=null, tableContent=
材料电导率/(S/m)
铜导体σcoil
金属元件σm(T)=1ρ01+αT-Tref
半导电屏蔽料σse=-9670T+877670
XLPE绝缘σXLPE=0.9×10-17exp0.1T+0.2×10-6E
聚丙烯1×10-18
聚乙烯1×10-18
石英玻璃1×10-14
), ArticleFig(id=1218262752179699789, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=CN, label=表2, caption=

脐带缆各层材料电导率

, figureFileSmall=null, figureFileBig=null, tableContent=
材料电导率/(S/m)
铜导体σcoil
金属元件σm(T)=1ρ01+αT-Tref
半导电屏蔽料σse=-9670T+877670
XLPE绝缘σXLPE=0.9×10-17exp0.1T+0.2×10-6E
聚丙烯1×10-18
聚乙烯1×10-18
石英玻璃1×10-14
), ArticleFig(id=1218262752259391569, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=EN, label=Table 3, caption=Material parameters of umbilical cable, figureFileSmall=null, figureFileBig=null, tableContent=
材料密度/(kg/m3)相对介电常数导热系数/(W/(m·K))比热容/(J/(kg·K))
铜8 9401400385
半导电屏蔽料1 0552.25102 405
交联聚乙烯9302.50.462 302
铅11 340135.3127
不锈钢7 920117.5475
镀锌钢丝7 850158475
聚丙烯9462.360.251 920
聚乙烯9352.250.462 302
石英玻璃2 2033.751.38703
), ArticleFig(id=1218262752364249177, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=CN, label=表3, caption=

脐带缆材料参数

, figureFileSmall=null, figureFileBig=null, tableContent=
材料密度/(kg/m3)相对介电常数导热系数/(W/(m·K))比热容/(J/(kg·K))
铜8 9401400385
半导电屏蔽料1 0552.25102 405
交联聚乙烯9302.50.462 302
铅11 340135.3127
不锈钢7 920117.5475
镀锌钢丝7 850158475
聚丙烯9462.360.251 920
聚乙烯9352.250.462 302
石英玻璃2 2033.751.38703
), ArticleFig(id=1218262752452329566, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=EN, label=Table 4, caption=Laying parameters and boundary conditions in different laying methods, figureFileSmall=null, figureFileBig=null, tableContent=
敷设方式敷设条件边界条件
土壤直埋d=1 m，土壤导热系数为1.0 W/(m·K)

第一类：Ta=20℃

第二类：q=0

第三类：Tf=30℃

h=12.5 W/(m2·K)

海底直埋d=1 m，土壤导热系数为1.0 W/(m·K)

第一类：Ta=15℃

第二类：q=0

第三类：Tf=30℃

h=6.5 W/(m2·K)

海底平铺d=0.1 m，土壤导热系数为1.0 W/(m·K)

第一类：Ta=15℃

第二类：q=0

第三类：Tf=20℃

h=6.5 W/(m2·K)

), ArticleFig(id=1218262752561381474, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=CN, label=表4, caption=

不同敷设方式下敷设参数与边界条件

, figureFileSmall=null, figureFileBig=null, tableContent=
敷设方式敷设条件边界条件
土壤直埋d=1 m，土壤导热系数为1.0 W/(m·K)

第一类：Ta=20℃

第二类：q=0

第三类：Tf=30℃

h=12.5 W/(m2·K)

海底直埋d=1 m，土壤导热系数为1.0 W/(m·K)

第一类：Ta=15℃

第二类：q=0

第三类：Tf=30℃

h=6.5 W/(m2·K)

海底平铺d=0.1 m，土壤导热系数为1.0 W/(m·K)

第一类：Ta=15℃

第二类：q=0

第三类：Tf=20℃

h=6.5 W/(m2·K)

), ArticleFig(id=1218262752657850472, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=EN, label=Table 5, caption=Comparison of ampacity calculation results under different laying methods, figureFileSmall=null, figureFileBig=null, tableContent=
敷设方式解析法载流量/A有限元法载流量/A相对误差/%
土壤直埋680.45677.27-0.47
海底直埋736.27726.40-1.34
海底平铺905.11878.30-2.96
), ArticleFig(id=1218262752724959340, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=CN, label=表5, caption=

不同敷设方式下载流量计算结果对比

, figureFileSmall=null, figureFileBig=null, tableContent=
敷设方式解析法载流量/A有限元法载流量/A相对误差/%
土壤直埋680.45677.27-0.47
海底直埋736.27726.40-1.34
海底平铺905.11878.30-2.96
), ArticleFig(id=1218262752821428339, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=EN, label=Table 6, caption=Physical parameters of umbilical cables at different seawater flow rates, figureFileSmall=null, figureFileBig=null, tableContent=
敷设方式海水流速/(m/s)导体温度/℃XLPE温度/℃XLPE电导率/(S/m)XLPE电场强度/(V/m)
海底直埋091.35890.7007.84×10-140.058 565
1×10-690.98790.3307.56×10-140.058 553
1×10-490.3389.6747.07×10-140.058 530
0.0290.10389.4486.92×10-140.058 523
0.190.189.4456.92×10-140.058 523
0.290.189.4446.91×10-140.058 522
1.090.189.4446.91×10-140.058 522
海底平铺091.56990.9118.00×10-140.058 572
1×10-690.69190.0347.34×10-140.058 542
1×10-487.55486.9045.36×10-140.058 431
0.0284.29483.6513.87×10-140.058 314
0.183.92183.2803.73×10-140.058 299
0.283.82383.1813.69×10-140.058 295
1.083.67983.0373.64×10-140.058 289
), ArticleFig(id=1218262752976617595, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590158446007116, language=CN, label=表6, caption=

不同海水流速下脐带缆的物理参数

, figureFileSmall=null, figureFileBig=null, tableContent=
敷设方式海水流速/(m/s)导体温度/℃XLPE温度/℃XLPE电导率/(S/m)XLPE电场强度/(V/m)
海底直埋091.35890.7007.84×10-140.058 565
1×10-690.98790.3307.56×10-140.058 553
1×10-490.3389.6747.07×10-140.058 530
0.0290.10389.4486.92×10-140.058 523
0.190.189.4456.92×10-140.058 523
0.290.189.4446.91×10-140.058 522
1.090.189.4446.91×10-140.058 522
海底平铺091.56990.9118.00×10-140.058 572
1×10-690.69190.0347.34×10-140.058 542
1×10-487.55486.9045.36×10-140.058 431
0.0284.29483.6513.87×10-140.058 314
0.183.92183.2803.73×10-140.058 299
0.283.82383.1813.69×10-140.058 295
1.083.67983.0373.64×10-140.058 289
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电-热-流多物理场耦合作用下脐带缆温度场及载流量计算研究
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范昌泓 , 娄敏 , 朱家星
绝缘材料 | 测试与分析 2024,57(9): 114-124
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绝缘材料 | 测试与分析 2024, 57(9): 114-124
电-热-流多物理场耦合作用下脐带缆温度场及载流量计算研究
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范昌泓, 娄敏, 朱家星
作者信息
  • 中国石油大学（华东） 石油工程学院，山东 青岛 266580

    • 范昌泓（1999-），男（汉族），福建大田人，硕士生，主要从事脐带缆多物理场耦合分析。

通讯作者:

娄敏（1981-），女（汉族），山东曲阜人，教授，博士，主要深水新型立管力学分析与优化设计、海洋管道流固耦合及振动抑制、深水柔性管道设计与研发研究。
Study on temperature field and ampacity calculation of umbilical cable under coupling of electro-thermal-fluid multi-physical fields
Changhong FAN, Min LOU, Jiaxing ZHU
Affiliations
  • School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, China
出版时间: 2024-09-20 doi: 10.16790/j.cnki.1009-9239.im.2024.09.012
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摘要
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脐带缆被誉为连接水下生产系统和上部设施的“神经生命线”，准确分析其温度场分布和载流量是安全开展海洋油气勘探和开采任务的关键保障。不同于传统海缆，脐带缆因结构复杂、功能多样，在位运行时存在复杂的电-热-流多物理场耦合效应，传统解析法难以确定其温度场分布和载流量。本文基于有限元软件Comsol建立脐带缆电-热-流多物理场耦合截面精细模型，通过控制变量法研究3种典型敷设方式、环境等因素对导体温度和稳态载流量的影响。结果表明：当电流较小时，影响脐带缆截面温度和稳态载流量的主导因素是管中液体温度；导体温度的变化趋势能够反映稳态载流量的变化情况；直埋时，埋设深度与外界流体温度的增加皆会削弱脐带缆的散热能力；平铺时，海水流动会明显降低脐带缆温度，在低流速下，流速增加对脐带缆的降温效果十分显著，但高流速的海水会在紧贴脐带缆的表面形成具有温度梯度的边界层，使热量的传递受到限制，降温效果反而不明显；绝缘老化对脐带缆整体温度分布的影响较小，但会影响截面最高温度。

脐带缆  /  电-热-流多场耦合  /  导体温度  /  载流量  /  环境因素  /  XLPE绝缘

Umbilical cables are known as the "nerve lifeline" connecting underwater production systems and upper facilities, and accurate analysis of their temperature field distribution and ampacity is a key guarantee for safe offshore oil and gas exploration and production tasks. Unlike traditional submarine cables, umbilical cables have complex electro-thermal-fluid multi-physical fields coupling effects due to their complex structure and diverse functions, and it is difficult to determine their temperature field distribution and ampacity by traditional analytical methods. A fine cross-sectional model of multi-field coupling of umbilical cable was established based on the finite element software COMSOL in this paper, and the influence of three typical laying methods, environment and other factors on the conductor temperature and steady-state ampacity was studied by the control variable method. The results show that when the current is small, the temperature of the fluid in tube is the dominant factor affecting the cross-sectional temperature and steady-state ampacity of umbilical cable. The trend of conductor temperature can reflect the change of steady-state ampacity. When buried directly, the increase of buried depth and the external fluid temperature will weaken the heat dissipation capacity of umbilical cable. When tiled, the seawater flow significantly reduces the temperature of umbilical cable, and at low flow rates, the increase of flow rate has a significant cooling effect on the umbilical cable. However, the high flow rate of seawater will form a boundary layer with temperature gradient on the surface close to the umbilical cable, making the heat transfer be restricted, and the cooling effect is not obvious. The insulation ageing has less influence on the overall temperature distribution of umbilical cable, but it affects the maximum temperature of the cross-section.

umbilical cable  /  electro-thermal-fluid multi-physical fields coupling  /  conductor temperature  /  ampacity  /  environmental factor  /  XLPE insulation
范昌泓, 娄敏, 朱家星. 电-热-流多物理场耦合作用下脐带缆温度场及载流量计算研究. 绝缘材料, 2024 , 57 (9) : 114 -124 . DOI: 10.16790/j.cnki.1009-9239.im.2024.09.012
Changhong FAN, Min LOU, Jiaxing ZHU. Study on temperature field and ampacity calculation of umbilical cable under coupling of electro-thermal-fluid multi-physical fields[J]. Insulating Materials, 2024 , 57 (9) : 114 -124 . DOI: 10.16790/j.cnki.1009-9239.im.2024.09.012
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0 引言
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在当前能源供需矛盾不断加重的情况下，海洋油气勘探与开采已成为世界能源产业和科技创新的聚焦点。然而，由于深水海域复杂的工作环境和条件，仅能传输电力、传递光信号的传统海洋电缆难以胜任海洋油气勘探和开采任务的要求。因此，脐带缆作为一种特殊类型的海缆应运而生，它能输送油气田开发所需的化学药剂，在全球范围内已被广泛应用，但我国长期依赖进口，对其分析设计、加工制造和安装敷设等关键技术的研究仍存在薄弱之处，制约了我国深海油气田的开发进程[1]。
研究脐带缆的温度场分布及其对载流量的影响是保障脐带缆安全运行的重要途径[2]。脐带缆在运行期间受强电作用产生温度场，同时受到外部复杂环境和自身物理场的耦合作用，对脐带缆载流量、综合性能的影响难以忽视[3]。另外，敷设方式与电缆群的布置方式同样影响电缆的温度场分布和载流量[4]，电缆的敷设位置不规范和回路数过于密集也会显著降低电缆的载流量[5-6]。上述影响因素的分析都是基于土壤直埋方式下展开，未考虑更为复杂的海底直埋、海底平铺等敷设方式。
目前国内外对脐带缆载流量以及多物理场耦合的研究较少，主要集中在传统海缆上。针对传统海缆多物理场耦合研究，T HENRIKSEN等[7]对大长度海缆进行电-热耦合分析，发现最高温度在J型管内，内部结构元件温度均接近极限温度，并根据结果开展了海缆的优化设计研究。G C KRIEGER等[8]对垂直浸入空气与海水界面的海缆进行模拟，分析了海缆在不同环境条件下的温度场分布。张凯等[9]针对挖沟敷设的电缆和接头建立数值模型，通过热分析确定温度过热的位置，为温度传感器的布置提供了建议。针对脐带缆多物理场耦合研究，D SHACKLETON等[10]将脐带缆简化为三芯模型进行电磁分析和热分析，指出边界条件是引起模拟结果不确定的主要原因。YANG Z X 等[11]和YAN J等[12-13]利用有限元软件建立脐带缆热弹性变形模型，引入热-力耦合分析方法，研究温度场对脐带缆材料和力学性能的影响，明确温度因素在脐带缆截面设计时难以忽略。
综上所述，现有针对脐带缆多物理场耦合研究主要集中在电-热耦合、热-力耦合等方面，由于脐带缆在位运行时内部传输光电信号、液体，同时受到外部海水、空气等环境因素的影响，存在复杂的电-热-流多物理场耦合效应，为保障脐带缆在位运行的安全可靠性，亟需开展脐带缆电-热-流多物理场耦合对其综合性能影响的研究。
本文针对现有研究的不足，以交流三芯交联聚乙烯（XLPE）绝缘铠装脐带缆为研究对象，综合考虑电-热-流多物理场耦合效应，构建脐带缆多物理场耦合截面精细模型，针对脐带缆在土壤直埋、海底直埋、海底平铺3种不同的敷设方式，开展脐带缆温度场分布与载流量研究，分析敷设方式、环境等因素对导体温度及稳态载流量的影响规律。
1 仿真模型建立
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1.1 脐带缆结构及尺寸
本文研究的脐带缆是一种交流三芯交联聚乙烯绝缘铠装脐带缆，主要由电缆单元、管单元、光纤单元、填充单元、铠装单元和护套单元组成，其结构名称及参数见表1，Comsol软件建立的脐带缆数值模型结构剖面见图1。
1.2 敷设方式
根据脐带缆的实际工程敷设，选取了包括土壤直埋、海底直埋和海底平铺的典型敷设方式进行仿真研究，敷设方式示意图见图2。
现有研究通常认为距脐带缆2 m范围以外的区域，其温度场分布不受脐带缆发热的影响[14]，因此将求解域的边界尺寸设为10 m×10 m，其中上部海水域高2 m，下部土壤域高8 m，海水域左侧为海水入口，右侧为出口。直埋时，脐带缆中心距离土壤表面距离d的取值区间为1.0～3.0 m[15]；平铺时，脐带缆放置在土壤表面，d取0.1 m。
2 模型方程
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2.1 控制方程
在实际工况中，脐带缆通电产生电磁场，导体和绝缘材料引起电损耗，散发热量改变周围温度。同时，导体电导率受温度影响，进一步导致导体电损耗和电磁场分布发生变化[16]。此外，外部环境的流体流动特性随温度变化而改变，同时流体场中的对流换热也会影响温度场的分布。在此过程中所涉及到的电磁场、传热场、流场和耦合场采用以下控制方程进行描述[17]。
（1）脐带缆通电后，电磁场控制方程为式（1）。
∇×H=JB=∇×AJ=σE+jωDE=-jωA
式（1）中：H为磁场强度，A/m；J为电流密度，A/m2；B为磁通密度，T；A为磁矢势，Wb/m；σ为电导率， S/m；E为电场强度，V/m；ω为角频率，rad/s；D为电位移矢量，C/m2。
在进行电-热耦合仿真时，需准确定义材料的电导率σ。Comsol软件支持二次开发，通过定义函数来描述导体电导率σcoil，使软件表达式计算出的导体有效交流电阻与国际电缆行业规范IEC 60287[18-20]定义的交流电阻值Rac(T)相匹配（见式（2）～式（8）），然后应用全局常微分方程对σcoil进行求解，为导体确定电导率σcoil，使导体电导率随温度发生变化。
RacT=ηRdc=ηR01+αT-Tref
R0=1Acoil⋅σ0
η=1+ys+yp
ys=xs4192+0.8xs4
xs2=8πfRdc10-7ks
yp=xp4dcs2192+0.8xp40.312dcs2+1.18xp4192+0.8xp4+0.27
xp2=8πfRdc10-7kp
式（2）～（8）中：η为交流电阻Rac与直流电阻Rdc之比；R0为20℃时的导体直流电阻，Ω/m；α为20℃时铜导体的电阻温度系数，取值为3.91×10-3℃-1；T为材料温度，℃；Tref为参考温度，取值为20℃；Acoil为导体实际横截面积，取值为800 mm2；σ0为20℃时导体的电导率，取值为5.96×107 S/m；ys为集肤效应因数；f为电源频率，取值为50 Hz；ks为常数，取值为1；yp为邻近效应因数；dc为导体屏蔽直径，mm；s为相邻导体轴线之间的距离，取值为68.8 mm；kp为常数，取值为0.8。
另外，假设脐带缆内部金属元件如铅护套、不锈钢管和镀锌钢丝铠装的电阻率呈线性变化，电导率与温度之间的关系如式（9）所示，通过应用线性电阻率，使金属元件具有温度依存性。
σm(T)=1ρ01+αT-Tref=σ01+αT-Tref
式（9）中：ρ0为20℃时材料的参考电阻率，Ω·m；σ0为20℃时材料的电导率，铅护套取值为4.55×106 S/m，不锈钢管取值为1.46×106 S/m，镀锌钢丝铠装取值为4.03×106 S/m；α是20℃时材料的电阻温度系数，铅护套取值为3.86×10-3℃-1，不锈钢管取值为5.77×10-3℃-1，镀锌钢丝铠装取值为5.31×10-3℃-1。
查阅相关文献[21]，针对脐带缆导体屏蔽和绝缘屏蔽材料的电导率σse以及绝缘层材料电导率σXLPE的计算式，选取了研究最广泛的经验式，见式（10）～（11）。
σse=-9670T+877670
σXLPE=σ0expaT+bE
式（10）～（11）中：σ0为XLPE的电导率，取值为0.9×10-17 S/m；a为电导率温度系数，取值为0.1℃-1；b为电导率电场强度系数，取值为0.2×10-6 m/V。
脐带缆各层材料电导率见表2。
（2）电磁场与传热场相互耦合的控制方程为式（12）。
ρCpu⋅∇T=∇⋅k∇T+QeQe=Qrh+QmlQrh=12ReJ⋅E*Qml=12RejωB⋅H*
式（12）中：ρ为材料密度，kg/m3；Cp为材料比热容， J/(kg·K)；u为速度，描述流体为矢量，描述固体为定值，m/s；k为材料导热系数，W/(m·K)；Qe为电磁热源，Qrh为电阻热源，Qml为磁滞热源，W/m³；E*为电场强度的共轭复数；H*为磁场强度的共轭复数；Re为共轭复数的实部。
（3）传热场分为脐带缆在土壤域中的固体传热以及在海水域中的流体传热。
土壤域中的固体传热控制方程为式（13）。
ρ1C1∂T∂t-k∇2T=Q1
式（13）中：ρ1为固体材料密度；C1为固体材料比热容；Q1为土壤域热源。
海水域中的流体传热控制方程为式（14）。
ρ2C2∂T∂t+u⋅∇T=-∇⋅q+τ:u∇-Tρ2∂ρ2∂Tp∂ρ2∂t+u⋅∇p+Q2
式（14）中：ρ2为流体材料密度；C2为流体材料比热容；q为传导热通量，W/m2；τ:u表示热-流耦合，流体非等温流动的过程；τ为粘滞应力张量，Pa；Q2为流体的热源；p为压强，Pa。
（4）流场控制方程为式（15）～（16）。
∇⋅ρ2u=0
ρ2u⋅∇u=-∇p+∇⋅μ∇u+∇uT-23μ∇⋅uI
式（15）～（16）中：μ为动力黏度，Pa·s；I为单位矩阵。
脐带缆材料在此过程中涉及到的相关物理场参数见表3。
2.2 边界条件
本文所建立的模型运用Comsol软件的AC/DC模块、传热模块和流体流动模块，参照脐带缆敷设方式（见图2）所定义的边界条件如下。
（1）AC/DC模块
本文采用电流激励导体线圈方式通电，通过在模块内置的“磁场”接口中使用“线圈”特征对导体施加线圈电流Icoil。
（2）传热模块
脐带缆传热过程中求解域的三类边界条件需要定义，土壤域下边界为深层土壤，其温度受脐带缆发热影响较小，将其设定为恒定温度Ta，即第一类边界条件；土壤左右边界理论为无限远，现有研究认为距脐带缆2 m范围以外区域的温度场分布不受其发热的影响，因此设土壤域左右边界的温度梯度q为0，即第二类边界条件；土壤直埋的土壤域上边界与空气热对流，海底直埋、海底平铺的海水域上边界与海水热对流，取传热系数为h，外界温度为Tf，模拟散热，即第三类边界条件。
（3）流体流动模块
规定海水域左边界处为入水口，海水自左向右平行流动，边界处流速（vw）为式（17）。
vw=-v0n
式（17）中：v0为海水初速度，m/s；n为单位方向向量。
为表示海水可以自由流动，规定海水域右边界为水流出口，其边界压强设为0，即式（18）。
p=0
为满足无滑移边界条件[22]，将海水在壁面处（海水域上下边界）的速度设为0，即式（19）。
vw=0
具体敷设条件与边界条件见表4[23]。
3 实例分析
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3.1 仿真结果验证分析
3.1.1 解析法计算稳态载流量
脐带缆稳态载流量的解析法参考国际电工委员会针对传统电缆制定的IEC 60287标准，该标准以等效热路模型为基础，将各层结构和外部环境简化为等效热阻，导体热损耗简化为等效热源，视电缆为一个由内到外传递热量的等效热路模型。对于结构复杂的脐带缆，可将规范定义的层间非金属层热阻T2进一步细分为各对应元件热阻T2～T5（见图3），从而更加精准地反映脐带缆内部结构，得到更准确的温度分布[24]。等效热阻法对于脐带缆稳态载流量的计算公式如式（20）所示。
I=Δθ-Wd0.5T1+nΔT2-5+ΔT6-7RT1+nR1+λ1ΔT2-5+1+λ1+λ2ΔT6-7
式（20）中：△T2-5=T2+T3+T4+T5，△T6-7=T6+T7；△θ为导体温度θc与环境温度θ0的差值，℃；Wd为绝缘介质损耗，W/m；T为等效热阻，K·m·W-1；n为导电线芯数，取值为3；λ1、λ2分别为铅护套和铠装层的介质损耗因数。
3.1.2 仿真结果验证分析
稳态载流量是导体温度达到90℃时的稳态工作电流，即电缆长期运行的持续额定电流[25]。通过比较解析法和有限元法对脐带缆稳态载流量的计算结果来验证模型准确性，计算结果见表5。由表5可知，两种方法的计算结果相近，最大相对误差小于3%，表明所建立的模型准确性良好。然而，需要指出的是，当前的理论模型并未考虑脐带缆内部钢管输送高温液体（约70℃的液压油）的情况。为了进一步研究这一问题，后续将在相同初始电流的情况下，对比截面最高温度，验证管内液体温度对脐带缆温度场分布的影响。
为避免理论分析因简化造成的结果误差，国内外许多专家学者采用了计算结果更为精确的数值计算法，如有限元法、有限差分法[26-27]，其中有限元法更适用于处理复杂几何形状和边界条件的问题，对结构及敷设环境复杂的脐带缆开展温度场分布及稳态载流量分析计算具有较高的准确性。因此，接下来使用有限元软件Comsol进一步对脐带缆进行仿真分析。
3.2 初始电流的影响
3.2.1 截面温度
以稳态载流量最低的土壤直埋方式为例，分析脐带缆截面最高温度与初始电流之间的关系，结果见图4，其中钢管内无液体的脐带缆可视为传统海缆。
由图4可知，传统海缆在初始电流为0时，其截面存在温度分布。这是由于截面温度受到外界温度的影响所致。此时土壤域下边界温度Ta小于上边界温度Tf，存在温度差，从而引发热交换过程。随着初始电流的增大，导体通电发热成为影响传统海缆温度分布的主导因素。对比发现，在初始电流小于200 A时，脐带缆截面的最高温度始终保持在70℃，这说明在该电流范围内，管内液体温度是影响脐带缆温度分布的主导因素，而非导体通电发热。而且，相比于传统海缆，脐带缆截面温度随电流变化的敏感性更低，稳态载流量也会更小，说明管内液体的存在不仅影响了截面最高温度，而且还影响了稳态载流量的大小。
为了确保脐带缆绝缘层处的温度不超过绝缘料XLPE的耐受范围（约为90℃），需要对XLPE绝缘料的温度分布展开研究。
3.2.2 XLPE绝缘温度
对脐带缆加载560～620 A电流，每20 A取1组结果值，研究不同初始电流下XLPE绝缘的温度分布情况，结果见图5。由图5可知，XLPE绝缘温度受电流影响较显著，随着电流增大，温度明显升高，为防止XLPE绝缘料因高温而损坏失效，后续开展脐带缆温度场分布及稳态载流量相关研究时，对导体加载初始电流600 A。
3.3 埋设深度的影响
直埋时，脐带缆的埋设深度d为1.0～3.0 m，比较脐带缆与传统海缆在土壤直埋和海底直埋敷设方式下导体温度和稳态载流量随埋设深度变化的规律，结果如图6所示，其中点线对应稳态载流量，柱状对应导体温度。由图6可知，随着埋设深度的增加，脐带缆和传统海缆的导体温度随之升高而稳态载流量随之下降，并且变化趋势逐渐变得平缓。其中在相同的埋设深度下，脐带缆的导体温度更高，稳态载流量更小，且对埋设深度的变化更不敏感。分析认为，随着埋设深度的增加，导体与土壤之间的传热路径变得更长，需要穿越更多的土壤与外界流体进行散热，因此散热性降低。
稳态载流量的变化趋势与导体温度相反，以土壤直埋敷设方式为例，针对不同埋设深度下脐带缆的导体温度与电导率之间的关系开展分析，结果见图7。由图7可知，导体的电导率与导体温度呈负相关关系，且两者变化趋势都随着埋设深度的增加逐渐平缓。电导率反映了物质传输电流的能力，当导体温度升高时，导体电导率减小，导致电流传输能力减弱，使得稳态载流量减小，因此导体温度与稳态载流量的变化趋势相反。
脐带缆在运行时的导体温度是影响其温度场分布的主要因素，也是确定载流量的核心依据[28]。同时，导体温度的变化趋势可以反映稳态载流量的变化情况，后续重点对导体温度展开分析。
3.4 海水段脐带缆温度场的影响因素分析
3.4.1 海水流速及温度的影响
对于海底直埋、海底平铺的敷设方式，海水流速取0～1.0 m/s，海水温度取17～32℃，计算不同海水流速、温度下的导体温度，结果见图8。当海水温度为20℃时，不同海水流速下的导体温度、XLPE绝缘层温度、电导率以及电场强度见表6。
从图8可以看出，相比海底直埋方式，在海底平铺敷设方式下脐带缆的导体温度受海水流速和海水温度的影响更加显著。这是因为海底平铺的脐带缆直接与海水接触发生热交换，相比之下，海底直埋的脐带缆埋设在土壤中，因此海水对其降温效果不如海底平铺敷设方式显著。此外，观察到脐带缆的导体温度随着海水温度升高而呈上升趋势，原因在于脐带缆热量的传递方式包括土壤热传导及海水对流热交换，对流换热能力与对流热通量和温度差相关，当海水温度升高时，温度差减小，从而散热性能降低，进而导致脐带缆导体温度升高。
同时从图8可以看出，海水流动对脐带缆的散热起到一定的促进作用。当海水流速小于0.02 m/s时，流速增加对脐带缆的散热效果明显，然而当海水流速大于0.02 m/s时，海水对脐带缆的降温效果受到限制。这是由于高速流动的海水会在紧贴脐带缆的表面形成具有温度梯度的边界层，热量在边界层的传递受到限制，使得脐带缆表面的热量很难有效地传递给更远处的海水，进而降低了降温效果。但需要指出的是，无论海水流速高低，海水的流动都对脐带缆的散热具有明显影响，尤其是在低流速下，海水流速增加对脐带缆的降温效果更加显著。
从表6可知，在海底直埋和海底平铺的敷设方式下，随着海水流速从0 m/s增加到1.0 m/s，XLPE温度分别降低了1.38%和8.66%，电导率分别降低了11.86%和54.5%，而电场强度仅分别降低了0.07%和0.48%，变化率明显低于前两者。其原因在于虽然XLPE绝缘电导率是关于温度与电场强度的函数（见表2），但本文研究对象为交流脐带缆，在交流状态下绝缘层电场分布主要由其材料的相对介电常数决定，而绝缘层温度对相对介电常数的影响可以忽略[29]。由此可见，XLPE绝缘的温度变化对其电场强度的影响极小，但却是影响XLPE电导率大小的主要因素。
3.4.2 自然流速下埋设深度的影响
由于海水流速一般不小于0.02 m/s[30]，在自然流速（0.1～1.0 m/s之间）下，脐带缆的导体温度变化基本上不会因海水流速改变而产生显著影响。为此进一步分析在自然流速下，不同埋设深度的脐带缆导体温度随海水温度的变化规律，结果见图9。
对比图9曲线斜率可以发现，由于脐带缆平铺时是直接浸泡在海水中，导体温度对海水温度变化的响应速度要比直埋方式更快。在海底直埋的敷设方式下，当脐带缆埋设深度相同时，海水在自然流速下对导体温度的影响微乎其微，曲线重叠，但随着埋设深度的增加，导体温度随海水温度变化的斜率逐渐降低。其原因在于随着埋设深度的增加，脐带缆所释放的热量需要穿过更多的土层才能传导到海水中。在此传导过程中，热量通过土壤的热传导会逐渐散发，剩余的热量减少，从而导致海水对导体温度的散热效果减弱，斜率逐渐下降。
3.5 XLPE绝缘老化的影响
在脐带缆的正常运行过程中，由于长时间高电压、高温等因素的联合作用，会导致其绝缘层老化。这种老化不仅会降低绝缘层的绝缘性能，还会降低其导热性能。假设XLPE绝缘材料的导热性能分别下降了30%、50%和70%，此时，其导热系数从0.46 W/(m·K)分别降低至0.32、0.23、0.14 W/(m·K)[31]。以海底直埋敷设方式为例，分析XLPE绝缘老化对脐带缆温度场分布的影响，结果见图10。
从图10可以看出，随着绝缘老化程度的增加，脐带缆截面最高温度升高，而最低温度几乎不变，且脐带缆整体温度分布的变化较小。造成这种现象的原因在于：脐带缆在传输电能的过程中导体会产生大量的热量，而绝缘层和其他内部构件的导热系数远小于铜导体的导热系数，使得热量由导体向外部发散。导体源源不断地产生热量，而随着绝缘层的导热性能下降，使得导体处的散热速率低于产热速率，导致热量在导体处积累，造成导体温度升高。而其他内部元件本身不产生热量，只是起到传热的作用，因此各元件温度变化较小，导致脐带缆整体温度分布变化不明显。
4 结论
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（1）海底平铺的脐带缆稳态载流量最大，此时脐带缆直接接触海水，热量容易传递，具有最佳的散热性。
（2）相较于传统海缆，脐带缆内部钢管输送高温液体，使截面温度随电流、环境参数变化的敏感性更低，不仅影响截面最高温度，还影响稳态载流量的大小。在初始电流小于200 A时，脐带缆截面最高温度始终保持在70℃，表明在此区间影响脐带缆温度分布的主导因素是管内液体温度而非导体通电发热。
（3）导体温度是确定载流量的关键依据，环境因素对脐带缆温度场分布与稳态载流量的影响不容忽视。脐带缆的埋设深度和海水温度会影响其散热能力，导致导体温度升高、电导率降低，减弱导体传输电流的能力，使得稳态载流量减小，造成导体温度与稳态载流量的变化趋势相反。
（4）海水流动对脐带缆的散热具有明显影响，在低流速下，海水流速增加对脐带缆的降温效果十分显著，而高流速下的海水会在紧贴脐带缆的表面形成具有温度梯度的边界层，热量在边界层的传递受到限制，导致流速增加所造成的降温效果反而不明显。
（5）当绝缘老化时，其导热性能下降，使得导体处的散热速率低于产热速率，导致热量积累，造成导体温度升高。而脐带缆内部其他元件不产生热量，仅起传热作用，各元件温度变化较小。因此，绝缘老化对脐带缆整体温度分布的影响较小，但随着绝缘老化程度的增加，脐带缆截面最高温度升高、稳态载流量降低。
基金
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  • 国家自然科学联合基金重点项目资助(U2006226)
文献
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2024年第57卷第9期
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doi: 10.16790/j.cnki.1009-9239.im.2024.09.012
  • 接收时间：2023-10-17
  • 首发时间：2025-12-24
  • 出版时间：2024-09-20
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  • 收稿日期：2023-10-17
  • 修回日期：2023-12-16
基金
国家自然科学联合基金重点项目资助(U2006226)
作者信息
    中国石油大学（华东） 石油工程学院，山东 青岛 266580

通讯作者:

娄敏（1981-），女（汉族），山东曲阜人，教授，博士，主要深水新型立管力学分析与优化设计、海洋管道流固耦合及振动抑制、深水柔性管道设计与研发研究。
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