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Article(id=1243879755850822627, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243879752042398333, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2024.08.005, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1708358400000, receivedDateStr=2024-02-20, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774493643962, onlineDateStr=2026-03-26, pubDate=1724083200000, pubDateStr=2024-08-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774493643962, onlineIssueDateStr=2026-03-26, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774493643962, creator=13701087609, updateTime=1774493643962, updator=13701087609, issue=Issue{id=1243879752042398333, tenantId=1146029695717560320, journalId=1240685776644648972, year='2024', volume='28', issue='8', pageStart='1133', pageEnd='1296', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774493643055, creator=13701087609, updateTime=1774493947997, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1243881031133147325, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243879752042398333, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1243881031133147326, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243879752042398333, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1175, endPage=1186, ext={EN=ArticleExt(id=1243879756131841001, articleId=1243879755850822627, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Experimental study on the combination of split heave point absorption wave energy converters and TLP type floating turbine, columnId=1241023037940748650, journalTitle=Journal of Ship Mechanics, columnName=Hydrodynamics, runingTitle=null, highlight=null, articleAbstract=

Effective use of numerous wave energy resources in the ocean remains a problem to be solved. Due to the wave conditions for low periodic and small wave height in the South China Sea, a model combining a split heave point absorber with a tension leg platform (TLP) was proposed. Through a physical model test, the hydrodynamic characteristics and wave energy capture efficiency of the split float were measured and analyzed, then compared with the whole float. And the optimal wave energy capture of the split float was discussed. The results show that the split float presents different hydrodynamic characteristics, and the energy capture efficiency of the device for small periodic waves is greatly improved in the low sea state, but the pitch motion of the platform is significantly increased in the specific wave direction, which requires further optimization of the tension leg system.

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面对海洋中庞大的波浪能资源，如何对其高效利用是目前仍需解决的一大难题。针对中国南海海域周期短、波高小的海况特点，本文提出一种与张力腿式平台（TLP）相结合的分块垂荡点吸收式波浪能装置模型。通过物理水池试验，测量分析分块浮子的水动力特性和波能捕获效率，同时与传统浮子的性能进行对比，探讨浮子分块后波浪能装置获能的优化效果。结果表明，分块浮子呈现出新的水动力特性，在低海况下装置对短周期波的能量捕获效率得到大幅提升，但在特定浪向角下会显著增大依附平台的纵摇运动，需要进一步优化张紧式系泊系统。

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通讯作者，E-mail：
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张茴栋（1984-），男，副教授

史宏达（1967-），男，教授，通讯作者，E-mail：。

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张茴栋（1984-），男，副教授

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张茴栋（1984-），男，副教授

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史宏达（1967-），男，教授，通讯作者，E-mail：。

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史宏达（1967-），男，教授，通讯作者，E-mail：。

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Energy Conversion and Management, 2021, 245: 114623., articleTitle=Experimental investigation of semi-submersible platform combined with point-absorber array, refAbstract=null), Reference(id=1243879771260695110, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243879755850822627, doi=null, pmid=null, pmcid=null, year=2020, volume=269, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[13], rfOrder=14, authorNames=Hu J, Zhou B, Vogel C, journalName=Applied Energy, refType=null, unstructuredReference=Hu J, Zhou B, Vogel C, et al. Optimal design and performance analysis of a hybrid system combing a floating wind platform and wave energy converters[J]. Applied Energy, 2020, 269: 114998., articleTitle=Optimal design and performance analysis of a hybrid system combing a floating wind platform and wave energy converters, refAbstract=null), Reference(id=1243879771365552715, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243879755850822627, doi=null, pmid=null, pmcid=null, year=2012, volume=29, issue=1, pageStart=89, pageEnd=114, url=null, language=null, rfNumber=[14], rfOrder=15, authorNames=Bachynski E E, Moan T, journalName=Marine Structures, refType=null, unstructuredReference=Bachynski E E, Moan T. Design considerations for tension leg platform wind turbines[J]. Marine Structures, 2012, 29(1): 89-114., articleTitle=Design considerations for tension leg platform wind turbines, refAbstract=null), Reference(id=1243879771449438800, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243879755850822627, doi=null, pmid=null, pmcid=null, year=2016, volume=93, issue=null, pageStart=87, pageEnd=100, url=null, language=null, rfNumber=[15], rfOrder=16, authorNames=Wan L, Gao Z, Moan T, Lugni C, journalName=Renewable Energy, refType=null, unstructuredReference=Wan L, Gao Z, Moan T, Lugni C. Experimental and numerical comparisons of hydrodynamic responses for a combined wind and wave energy converter concept under operational conditions[J]. 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ArticleFig(id=1243879767133499791, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243879755850822627, language=EN, label=Tab.1, caption=

Parameters of NREL 5MW wind turbine

, figureFileSmall=null, figureFileBig=null, tableContent=
设计参数原型模型设计参数原型模型
风轮直径/m1262.52机舱质量/kg2400001.92
塔架高度/m901.8塔架质量/kg3470002.776
叶片质量/kg1100000.88总质量/kg6970005.576
), ArticleFig(id=1243879767276106133, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243879755850822627, language=CN, label=表1, caption=

NREL 5MW风机参数

, figureFileSmall=null, figureFileBig=null, tableContent=
设计参数原型模型设计参数原型模型
风轮直径/m1262.52机舱质量/kg2400001.92
塔架高度/m901.8塔架质量/kg3470002.776
叶片质量/kg1100000.88总质量/kg6970005.576
), ArticleFig(id=1243879767393546651, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243879755850822627, language=EN, label=Tab.2, caption=

Platform parameters

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设计参数原型模型设计参数原型模型
浮筒直径/m350.7吃水/m250.5
浮筒高度/m70.14伸臂尺寸/m4×3×150.08×0.06×0.3
中心底柱直径/m60.12阻尼板尺寸/m15×100.3×0.2
底柱高度/m180.36排水体积/m36,3245.06×10-2
导轨直径/m10.2总质量/kg2.525×10620.2
导轨长度/m400.8
), ArticleFig(id=1243879767506792863, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243879755850822627, language=CN, label=表2, caption=

平台参数

, figureFileSmall=null, figureFileBig=null, tableContent=
设计参数原型模型设计参数原型模型
浮筒直径/m350.7吃水/m250.5
浮筒高度/m70.14伸臂尺寸/m4×3×150.08×0.06×0.3
中心底柱直径/m60.12阻尼板尺寸/m15×100.3×0.2
底柱高度/m180.36排水体积/m36,3245.06×10-2
导轨直径/m10.2总质量/kg2.525×10620.2
导轨长度/m400.8
), ArticleFig(id=1243879767624233380, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243879755850822627, language=EN, label=Tab.3, caption=

Float parameters

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设计参数原型模型
外径/m200.4
内径/m80.16
高度/m100.20
吃水/m50.10
质量/kg3×2612633×2.421
分块间隙/cm400.8
), ArticleFig(id=1243879767741673898, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243879755850822627, language=CN, label=表3, caption=

浮子模型参数

, figureFileSmall=null, figureFileBig=null, tableContent=
设计参数原型模型
外径/m200.4
内径/m80.16
高度/m100.20
吃水/m50.10
质量/kg3×2612633×2.421
分块间隙/cm400.8
), ArticleFig(id=1243879767905251759, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243879755850822627, language=EN, label=Tab.4, caption=

Damping parameters of air damper

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编号F0F1F2F3
D/（N·s2·m-2）00.7221.9782.621
), ArticleFig(id=1243879768014303668, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243879755850822627, language=CN, label=表4, caption=

空气阻尼器阻尼参数

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编号F0F1F2F3
D/（N·s2·m-2）00.7221.9782.621
), ArticleFig(id=1243879768140132794, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243879755850822627, language=EN, label=Tab.5, caption=

Parameters of regular and irregular waves

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规则波不规则波
编号周期T/s波高H/m编号谱峰周期Tp/s有义波高Hs/m
LC10.70.02ILC10.90.04
LC20.80.025ILC21.10.04
LC30.90.035ILC31.30.04
LC41.00.04ILC41.50.04
LC51.10.05ILC51.70.04
LC61.20.06ILC61.30.05
LC71.30.07ILC71.30.06
LC81.40.08ILC81.30.07
LC91.50.08
LC101.60.08
LC111.70.08
LC121.80.08
), ArticleFig(id=1243879768261767617, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243879755850822627, language=CN, label=表5, caption=

规则波和不规则波参数

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规则波不规则波
编号周期T/s波高H/m编号谱峰周期Tp/s有义波高Hs/m
LC10.70.02ILC10.90.04
LC20.80.025ILC21.10.04
LC30.90.035ILC31.30.04
LC41.00.04ILC41.50.04
LC51.10.05ILC51.70.04
LC61.20.06ILC61.30.05
LC71.30.07ILC71.30.06
LC81.40.08ILC81.30.07
LC91.50.08
LC101.60.08
LC111.70.08
LC121.80.08
), ArticleFig(id=1243879768395985352, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243879755850822627, language=EN, label=Tab.6, caption=

Test cases

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编号浮子类型波浪方向PTO阻尼力
D0S0°F0、F1、F2、F3
D45S45°F0、F1、F2、F3
D90S分块90°F0、F1、F2、F3
D135S135°F0、F1、F2、F3
D180S180°F0、F1、F2、F3
D0W整块0°F0、F1、F2、F3
), ArticleFig(id=1243879768509231565, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243879755850822627, language=CN, label=表6, caption=

测试工况

, figureFileSmall=null, figureFileBig=null, tableContent=
编号浮子类型波浪方向PTO阻尼力
D0S0°F0、F1、F2、F3
D45S45°F0、F1、F2、F3
D90S分块90°F0、F1、F2、F3
D135S135°F0、F1、F2、F3
D180S180°F0、F1、F2、F3
D0W整块0°F0、F1、F2、F3
), ArticleFig(id=1243879768605700560, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243879755850822627, language=EN, label=Tab.7, caption=

Maximum energy capture ratio under different incident wave directions(%)

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阻尼力浪向
D0SD45SD90SD135SD180S
F118.9017.2720.6217.5717.93
F222.2416.5421.1215.5718.13
F317.1914.6415.0415.2716.62
), ArticleFig(id=1243879768731529686, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243879755850822627, language=CN, label=表7, caption=

不同浪向下最大获能比（%）

, figureFileSmall=null, figureFileBig=null, tableContent=
阻尼力浪向
D0SD45SD90SD135SD180S
F118.9017.2720.6217.5717.93
F222.2416.5421.1215.5718.13
F317.1914.6415.0415.2716.62
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Statistics of energy capture of split float under different damping forces (Unit: ×10-2 W)

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ILC1ILC2ILC3ILC4ILC5ILC6ILC7ILC8
F17.09316.08322.14917.32013.78724.16128.95638.021
MaxF28.78619.72326.93320.54919.27628.54732.58339.652
F38.47215.51920.62419.54819.28425.38932.05638.787
F10.7561.0101.5571.6161.4731.5912.0192.496
MeanF20.9441.0851.6881.9092.1692.4353.7064.012
F30.8231.0311.5871.8431.8511.6522.3413.161
F10.7261.6701.9712.2691.8972.4304.3034.481
StdF21.1252.0463.1973.7883.5953.3044.7484.950
F30.7562.0052.5132.7773.4392.8034.6734.588
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不同阻尼力下分块浮子获能的统计值（单位：×10-2 W）

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F17.09316.08322.14917.32013.78724.16128.95638.021
MaxF28.78619.72326.93320.54919.27628.54732.58339.652
F38.47215.51920.62419.54819.28425.38932.05638.787
F10.7561.0101.5571.6161.4731.5912.0192.496
MeanF20.9441.0851.6881.9092.1692.4353.7064.012
F30.8231.0311.5871.8431.8511.6522.3413.161
F10.7261.6701.9712.2691.8972.4304.3034.481
StdF21.1252.0463.1973.7883.5953.3044.7484.950
F30.7562.0052.5132.7773.4392.8034.6734.588
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Statistics of energy capture of split float under different wave directions (Unit: ×10-2 W)

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ILC1ILC2ILC3ILC4ILC5ILC6ILC7ILC8
MaxD0S8.78619.72326.93325.54919.27628.54732.58339.652
D45S7.61717.85925.10426.20520.77128.16333.62039.013
D90S8.56017.18124.90826.48918.75227.13231.98636.625
D135S8.32616.40024.19727.49418.27926.46531.28135.467
D180S7.08517.24322.17126.61317.31827.39931.42537.473
D0W7.04216.27922.83727.73119.26325.88430.79236.066
MeanD0S0.9441.0851.6881.9092.1692.4353.7064.012
D45S0.8611.0061.5741.8321.4022.1593.4483.865
D90S0.8861.1301.6731.9611.9172.1923.2023.720
D135S0.8231.0761.5461.8641.8512.1153.0873.604
D180S0.7291.0471.4231.7501.6242.0673.0823.796
D0W0.6250.9221.0531.7401.8331.6152.5943.072
StdD0S1.1252.0463.1973.7883.5953.3044.7484.950
D45S0.8232.0442.5243.9543.0403.0774.1224.434
D90S0.9052.0242.1083.3013.0392.7253.7784.167
D135S0.7701.3392.2473.7993.2522.3502.6383.026
D180S0.7281.4871.7702.5892.2052.4192.8713.128
D0W0.6031.4541.9852.7492.5462.3432.4532.875
), ArticleFig(id=1243879769180320234, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243879755850822627, language=CN, label=表9, caption=

不同来浪方向时浮子获能统计值（单位：×10-2 W）

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ILC1ILC2ILC3ILC4ILC5ILC6ILC7ILC8
MaxD0S8.78619.72326.93325.54919.27628.54732.58339.652
D45S7.61717.85925.10426.20520.77128.16333.62039.013
D90S8.56017.18124.90826.48918.75227.13231.98636.625
D135S8.32616.40024.19727.49418.27926.46531.28135.467
D180S7.08517.24322.17126.61317.31827.39931.42537.473
D0W7.04216.27922.83727.73119.26325.88430.79236.066
MeanD0S0.9441.0851.6881.9092.1692.4353.7064.012
D45S0.8611.0061.5741.8321.4022.1593.4483.865
D90S0.8861.1301.6731.9611.9172.1923.2023.720
D135S0.8231.0761.5461.8641.8512.1153.0873.604
D180S0.7291.0471.4231.7501.6242.0673.0823.796
D0W0.6250.9221.0531.7401.8331.6152.5943.072
StdD0S1.1252.0463.1973.7883.5953.3044.7484.950
D45S0.8232.0442.5243.9543.0403.0774.1224.434
D90S0.9052.0242.1083.3013.0392.7253.7784.167
D135S0.7701.3392.2473.7993.2522.3502.6383.026
D180S0.7281.4871.7702.5892.2052.4192.8713.128
D0W0.6031.4541.9852.7492.5462.3432.4532.875
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基于TLP浮式风机的分块垂荡点吸式波浪能装置的实验研究
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张茴栋 , 许聪 , 史宏达
船舶力学 | 流体力学 2024,28(8): 1175-1186
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船舶力学 | 流体力学 2024, 28(8): 1175-1186
基于TLP浮式风机的分块垂荡点吸式波浪能装置的实验研究
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张茴栋, 许聪, 史宏达
作者信息
  • 中国海洋大学，山东　青岛　266100

    • 张茴栋（1984-），男，副教授

    史宏达（1967-），男，教授，通讯作者，E-mail：。

通讯作者:

通讯作者，E-mail：
Experimental study on the combination of split heave point absorption wave energy converters and TLP type floating turbine
Hui-dong ZHANG, Cong XU, Hong-da SHI
Affiliations
  • Ocean University of China, Qingdao 266100, China
出版时间: 2024-08-20 doi: 10.3969/j.issn.1007-7294.2024.08.005
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摘要
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面对海洋中庞大的波浪能资源，如何对其高效利用是目前仍需解决的一大难题。针对中国南海海域周期短、波高小的海况特点，本文提出一种与张力腿式平台（TLP）相结合的分块垂荡点吸收式波浪能装置模型。通过物理水池试验，测量分析分块浮子的水动力特性和波能捕获效率，同时与传统浮子的性能进行对比，探讨浮子分块后波浪能装置获能的优化效果。结果表明，分块浮子呈现出新的水动力特性，在低海况下装置对短周期波的能量捕获效率得到大幅提升，但在特定浪向角下会显著增大依附平台的纵摇运动，需要进一步优化张紧式系泊系统。

分块点吸收式  /  波浪能装置  /  浮式风机平台  /  物理模型试验  /  获能效率

Effective use of numerous wave energy resources in the ocean remains a problem to be solved. Due to the wave conditions for low periodic and small wave height in the South China Sea, a model combining a split heave point absorber with a tension leg platform (TLP) was proposed. Through a physical model test, the hydrodynamic characteristics and wave energy capture efficiency of the split float were measured and analyzed, then compared with the whole float. And the optimal wave energy capture of the split float was discussed. The results show that the split float presents different hydrodynamic characteristics, and the energy capture efficiency of the device for small periodic waves is greatly improved in the low sea state, but the pitch motion of the platform is significantly increased in the specific wave direction, which requires further optimization of the tension leg system.

split heave point absorption  /  wave energy converter  /  floating turbine platform  /  physical model test  /  energy capture efficiency
张茴栋, 许聪, 史宏达. 基于TLP浮式风机的分块垂荡点吸式波浪能装置的实验研究. 船舶力学, 2024 , 28 (8) : 1175 -1186 . DOI: 10.3969/j.issn.1007-7294.2024.08.005
Hui-dong ZHANG, Cong XU, Hong-da SHI. Experimental study on the combination of split heave point absorption wave energy converters and TLP type floating turbine[J]. Journal of Ship Mechanics, 2024 , 28 (8) : 1175 -1186 . DOI: 10.3969/j.issn.1007-7294.2024.08.005
正文
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0　引言
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鉴于海风与海浪的天然相关性，许多学者提出了将波浪能装置（wave energy converter，WEC）与海上风机相结合的概念，通过共享支撑平台以及电力传输系统的方式分摊装置的成本，从而提高海洋能开发的经济效益[1]。目前，海上浮式风机依据其基础平台大致可分为立柱式、张力腿式和半潜式三种类型[2]，与之对应的波浪能装置则有上百种之多，但大部分组合装置仍然处于概念研究阶段。
基于Spar风机平台，Wan等[3]提出与振荡浮子式波浪能装置相结合的模型，对比了两个水池的物模实验结果，发现除共振周期附近立柱与WEC之间的交界力存在较大差异以外，两种实验条件下的结果非常接近；Li等[4]提出进一步集成潮流能的复合装置，可减小风机平台的纵荡与纵摇运动，同时总功率可提高45%。
针对张力腿式风机平台，Ren等[5]提出一种附加振荡浮子式波浪能装置的组合模型，发现波浪单独作用时，WEC会明显改变平台纵荡和垂荡的运动幅值，叠加定常风荷载后，平台纵摇的波动范围会显著减小。
结合半潜浮式风机平台，Li等[6]运用开源代码对圆环形点吸收式风浪联合模型进行了动力耦合分析，并与AWQA模拟结果对比，验证其结论的准确性；Wang等[7]在此基础上分析了WEC形状对装置的运动响应和获能效率产生的影响，发现平台的运动受浮子的干扰较小，凹形波浪能装置的获能效率最优；Si等[8]发现不同的PTO阻尼控制方法对平台水动力特性有显著影响，其中无功控制有最高的波能捕获效率；Chen等[9]将主动Bang-Bang控制运用于组合模型，结果表明其能有效降低平台运动响应并提升WEC功率；Zhang等[10]将OWC与半潜式平台相结合，并对比4种不同PTO控制方法对装置的影响，发现增益调度控制能够明显降低平台的运动响应；Gao等[11]在典型的PTO系统上分析了两种机械储能系统对WEC的影响，指出两者均能有效增加WEC的获能，并且降低了功率波动。
为进一步提升装置的波能捕获效率，Sun等[12]将波浪能装置进行阵列化，发现WEC阵列会增加平台的纵摇和垂荡，但抑制纵荡响应，浮子的交错排列更有利于WEC能量捕获；Hu等[13]发现高频区域复合结构的辐射阻尼和附加质量对浮子参数较为敏感，大尺寸的少量浮子可捕获更多的能量，但是单位质量的捕获效率无太大差异。
综上所述，波浪能装置与浮式风机结合后会改变原结构的运动响应，影响的范围和程度取决于组合装置的形式和布局。波浪能的贡献增加了装置整体获能效率，可提高经济效益。然而，目前大多组合设计适用于波浪周期较长的海况，很难应用于周期较短、波高较小的中国周边海域。为了更好地吸收此类波浪的能量，本文提出一种基于张力腿式平台（TLP）的分块垂荡点吸收式波浪能装置，通过物理水池试验，开展一系列分块浮子的水动力耦合特性的分析和波能捕获效率的研究，探讨其相对于传统浮子组合装置的优缺点，为中国海域波浪能资源的开发提供参考。
1　试验模型及工况设计
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1.1　试验模型
1.1.1　风机
试验参数设计采用重力相似准则，缩尺比为1:50。模型实物如图1所示，总体分为三个部分：①风机；②平台基础；③波浪能装置，分别对应图1（a）标号。
本文采用NREL 5MW风机作为原型，具体参数如表1所示。由于本实验主要研究分块浮子以及平台的水动力特性，因此对上部风机结构进行了简化处理，主要保证风机质量和重心高度与实际情况一致。
1.1.2　平台
参考前人所提出的浮式风机新型张力腿平台，同时结合相关设计的要求[14]，本文针对5 MW风机的平台结构进行了优化改进，新平台（见图1（b））的构成可分为四个部分：④浮筒及伸臂；⑤中心柱；⑥导轨和⑦阻尼板，分别与图1（b）中各编号对应，各构件尺寸参数如表2所示。
1.1.3　浮子
如图2所示，分块浮子为3个圆心角为120°的扇形浮子，并且可以通过顶部和底部的螺栓连接为一个整体，同步开展相关的对照试验，具体模型参数见表3。
1.1.4　PTO系统
PTO（power take-off）系统采用空气阻尼器模拟（图3），通过调节气阀开口的大小控制施加阻尼的幅值。将气缸中的气体简化为理想气体模型，根据公式（1）可求得气缸阻尼参数D[15]，计算结果见表4。
1.1.5　试验水池布置及系泊系统
物理模型试验地点为山东省海洋工程重点实验室，波浪水槽的平面尺寸为60 m×3 m，实验水深为1 m，整体布局见图4，分别在装置前方和侧面放置两根波高仪用于记录波面时程曲线，共测试五个来浪方向：0°、45°、90°、135°和180°。系泊形式如图5所示采取斜向45°系泊，即张力腿与锚固点底面的夹角为45°。张力腿由弹簧与钢绞线组合而成，弹簧刚度系数为21.3 N/mm。
1.2　工况设计
试验内容主要包括浮子静水衰减试验、规则波和不规则波试验，具体波浪参数见表5，其中，0.7~1.0 s的波况对应中国领海的常见海况。规则波和不规则波的测试时长分别为120 s和200 s。不规则波采用JONSWAP谱，谱峰升高因子为3.0。装置测试的工况如表6所示，依据浮子类型、浪向和PTO阻尼力进行组合，对于整块浮子只开展0°浪向的测试实验。
2　试验结果分析
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2.1　自由衰减试验
自由衰减试验主要测量两类浮子的垂荡共振周期，其衰减曲线如图6所示，根据该曲线可知，浮子分块后垂荡共振周期由1.08 s（图6（a））减小至0.82 s（图6（b））。结合中国周边海况可知，分块浮子共振周期值处于其主要波浪周期范围中间，这也是本模型尺寸设计的主要依据之一。
2.2　规则波试验
2.2.1　浮子相对垂荡运动
由于PTO系统只在垂荡方向上摄取波浪能，因此重点研究浮子与平台之间的相对垂荡运动。图7（a）展示了0°来浪条件下施加四种PTO阻尼力时，浮子相对垂荡运动的响应幅值随波浪周期的变化规律，其它方向类同。显然其响应存在两个峰值，但成因迥然不同。为了便于描述，这里定义第一共振区（0.7~1.4 s）和第二共振区（1.4~1.8 s）。第一共振区发生共振是由波浪激励频率接近浮子的固有频率所引起；对于第二共振区，研究过程中发现，当不附加WEC时，纯平台的运动响应均随周期呈均匀递增趋势，而引入WEC后，平台响应会在1.5 s处出现峰值（见2.2.3节），因此推断其成因是浮子和平台发生了相互耦合作用。此外，PTO阻尼力仅明显改变浮子垂荡响应第一共振周期的位置，其周期值随阻尼力的增大而增大，而对第二共振周期影响并不明显。
图7（b）给出了来浪方向对分块浮子垂荡运动产生影响的规律（以F0为例）。当分块浮子处于迎浪侧，且水平中线与浪向重合时（D0S），响应幅值最大，在0.8 s发生共振运动。其余来浪方向时，由于中柱的遮蔽效应及浮子迎浪投影面积的变化，发生共振的周期变大，相对垂荡运动的幅值变小，即便如此，在短周期（0.7~1.0 s）时大部分浪向下分块浮子运动响应性能依然优于整块浮子（D0W）。另外浪向不会明显改变第二共振周期的位置。
2.2.2　浮子获能效率
图8为0°来浪条件下，不同PTO阻尼力时浮子获能比随激励周期变化的规律。与预期一致，获能比也存在两个峰值。分块浮子（D0S）获能比第一峰值对应的周期随阻尼力增大而增大，但其峰值的幅度在F2时达到最大，表示此阻尼力接近最优阻尼。对于第二共振区，PTO阻尼力的大小对分块浮子获能的影响不大。
此外，在短周期条件下，即第一共振区，分块浮子获能表现明显优于整块浮子，但此周期范围随PTO阻尼力的增大而逐渐减小，说明分块浮子对于短周期波在较小PTO阻尼时有更好的能量捕获效果；对于长周期波，即第二共振区，整块浮子获能比较大，再次印证分块浮子更加适用于中国周边的海域。
表7列举了不同浪向下分块浮子在第一共振区的最大获能比。浪向的差异导致分块浮子在同一PTO阻尼力下最大获能比出现明显不同。因系泊方式及分块浮子空间布局的共同影响，最大获能比出现在0°来浪方向上，而45°和135°时获能通常较低。分块浮子并不具有整块浮子的对称形状，因此可推知其最大获能比出现的周期会随浪向而发生一定的改变。综合比较所有获能比可知，最优阻尼并不因浪向的变化发生太大的改变，但对系泊方式较为敏感。
2.2.3　平台运动响应
图9和图10展示了平台在不同条件下纵荡和纵摇的运动响应，总体来说，随着波浪激励周期的增大，平台纵荡和纵摇的响应幅值会逐渐增大。由图9进一步可知，分块浮子在不同PTO阻尼力条件下摄取能量时，除个别工况外，大部分情况下并不会显著改变平台的纵荡和纵摇的响应幅值，即PTO阻尼力的大小对平台水动力性能的改变并不大。
由图10可知，平台运动在短周期波时对来浪方向并不敏感，在长周期波时会出现明显差异，45°和135°来浪方向上的幅值一直较大，显然是由系泊方式所致，此时来浪方向与其中两条系泊线水平投影重合，无法提供足够的稳定性，导致平台运动响应加剧。与整块浮子相比（D0W），总体上讲分块浮子在不同来浪方向下，并未对所依附平台的纵荡运动产生显著的改变，但是在较长周期时明显增加了纵摇运动的幅值。
2.3　不规则波试验
2.3.1　浮子相对垂荡运动
由图11（a）可知，有义波高一定时，随着谱峰周期的增大，相对垂荡运动响应的各个统计参量会逐渐增大。而当谱峰周期一定时（图11（b）），响应幅值也会随有义波高的增大而增大，但其增长的速率会逐渐降低，此特点在最大和最小响应幅值中尤为明显。图11（c）为ILC3工况时，不同PTO阻尼力下浮子垂荡响应统计值，无阻尼情况下（F0）垂荡响应最剧烈，稍微施加阻尼后，响应幅值会大幅减小，当阻尼力成倍增加后（表8），相对垂荡运动的统计值并未成比例减小。图11（d）展示了同一工况下不同浪向对浮子相对垂荡运动的影响，在D0S时，垂荡响应最剧烈，这与规则波的结论一致。虽然各个入射角度下，分块浮子的相对垂荡运动有所差异，但其幅值都比整块浮子（D0W）的大，进一步论证了分块浮子在不规则海况中运动的优越性。
2.3.2　浮子获能效率
对于不规则波获能效率，我们将从WEC获能的最大值（Max）、均值（Mean）和标准差（Std）来进行讨论。
表8展示不同阻尼力时，各个工况下分块浮子（D0S）获能的统计值。整体上，浮子俘获波浪能的均值和标准差均随谱峰周期和有义波高的增加而呈增大趋势。F2阻尼力下，浮子获能的统计值基本上都高于其它两种阻尼时的获能，说明F2此时最接近分块浮子的最优获能阻尼，与规则波的规律一致。
表9对比了F2阻尼力时不同来浪方向下分块浮子的能量获取效果。在小周期的不规则海况中，分块浮子获能的统计值在各个浪向下基本都高于整块浮子，表明分块浮子对不规则短波的获能更优，随着谱峰周期的进一步增大，部分浪向下整块浮子获能的表现更佳。实际上，不规则波海况中来浪方向对分块浮子获能的影响与规则波中的结论类似，不再赘述。
2.3.3　平台运动响应
以D0S为例，图12（a）~（b）分析了浮子施加不同PTO阻尼力后对平台运动产生的影响。虽然此工况下，阻尼力的存在可以改变平台纵荡和纵摇运动的极值，但整体上看，各个阻尼力作用时均值和标准差的差异并不太大，意味着多数情况下，不规则波中PTO阻尼力对平台运动的影响并不显著。图12（c）~（d）对比了不同浪向的影响，尽管45°和135°的入射方向上平台响应略大，但总体上不同浪向下响应的差异并不太大。与整块浮子相比，无论哪种入射方向，分块浮子都会增大平台的纵摇运动。
2.3.4　谱分析
图13从频谱的角度揭示了不同PTO阻尼力和浪向对浮子相对垂荡运动的影响。从图13（a）可看出，随着PTO阻尼力的增加，浮子相对垂荡运动谱峰值明显降低。PTO阻尼力使谱峰频率向低频移动，进一步增大阻尼力后，谱峰周期围绕1.5 s发生小幅摄动，依据规则波中分析可知，该周期接近第二共振区间的共振周期，阻尼力对其影响较小；从图13（b）可知，浪向使分块浮子相对垂荡运动的谱峰频率有所差异，但无论何种来浪方向，分块浮子对高频部分（短周期波）能量的摄取明显优于整块浮子，同时分块浮子响应的零阶谱矩在各个浪向下始终大于整块浮子，说明浮子分块后可摄取更多的不规则波能量。
图14（a）、（c）显示了不同阻尼力下平台纵荡、纵摇运动的频谱图对比。谱峰频率位置的变化规律与图13（a）中基本一致，由于阻尼力的存在，零阶谱矩有所减小，主要是通过降低高频部分的响应来实现的。整体上看，平台运动受分块浮子PTO阻尼力的影响有限。
图14（b）、（d）针对浪向的影响进行了探讨，谱峰频率的位置均随来浪方向的改变而发生小幅的移动。对于纵荡，45°和135°来浪时零阶谱矩较大，此时分块浮子相对整块的制荡效果并不明显。对于纵摇，分块后各个浪向下，平台在高频和低频处响应均会增加，致使平台运动幅度增大，且在45°和135°时出现双峰现象，显然与系泊方式有关。
3　结论
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为有效获取中国周边海域的波浪能，本文提出了一种基于TLP浮式风机平台的分块垂荡点吸收式波浪能装置模型，通过物理水池试验的方法，重点研究了分块浮子在规则波及不规则波中的水动力性能及获能效率，探讨了来浪方向和PTO阻尼力所带来的影响，分析了浮子分块后对平台的运动所产生的影响，得出以下结论：
（1）分块浮子相对垂荡运动的RAO会出现两个共振区间，然而其产生的机制并不相同，PTO阻尼力和来浪方向只能改变分块浮子在第一共振区间的共振周期。
（2）对于短周期波，浮子分块后的获能比明显高于整块浮子，但随着PTO阻尼力的增大，性能优越的周期区间范围会逐渐减小。由于系泊方式和分块浮子空间布局的共同作用，来浪方向会明显改变浮子的获能比。
（3）在不规则波工况中，无论何种来浪方向，分块浮子都可以很好地摄取高频部分的能量，且其相对垂荡运动的零阶谱矩始终大于整块浮子。分块浮子在特定的来浪和系泊条件下会大幅加剧平台的纵摇，甚至在频谱中产生双峰现象，相比之下，对平台纵荡的影响并不显著。
基金
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  • 国家自然科学基金资助项目(52271337; 51809244; 52071303)
  • 山东省自然科学基金项目(ZR2019BEE042)
文献
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2024年第28卷第8期
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doi: 10.3969/j.issn.1007-7294.2024.08.005
  • 接收时间：2024-02-20
  • 首发时间：2026-03-26
  • 出版时间：2024-08-20
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  • 收稿日期：2024-02-20
基金
国家自然科学基金资助项目(52271337; 51809244; 52071303)
山东省自然科学基金项目(ZR2019BEE042)
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    中国海洋大学，山东　青岛　266100

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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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