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Article(id=1242150713795616870, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1242150711367119505, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2024.04.004, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1695052800000, receivedDateStr=2023-09-19, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774081408213, onlineDateStr=2026-03-21, pubDate=1713542400000, pubDateStr=2024-04-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774081408213, onlineIssueDateStr=2026-03-21, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774081408213, creator=13701087609, updateTime=1774081408213, updator=13701087609, issue=Issue{id=1242150711367119505, tenantId=1146029695717560320, journalId=1240685776644648972, year='2024', volume='28', issue='4', pageStart='479', pageEnd='636', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1774081407634, creator=13701087609, updateTime=1774081679149, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1242151850229702738, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1242150711367119505, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1242151850229702739, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1242150711367119505, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=513, endPage=526, ext={EN=ArticleExt(id=1242150714017914983, articleId=1242150713795616870, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Pitch mitigation characteristics of floating offshore wind turbine substructures with tuned liquid multi-column damper (TLMCD), columnId=1241023037940748650, journalTitle=Journal of Ship Mechanics, columnName=Hydrodynamics, runingTitle=null, highlight=null, articleAbstract=

With a scale model of tuned liquid multi-column damper (TLMCD) and floating substructure established, experiments were carried out in a flume to study the control effect of TLMCD on the pitch motion response of the floating foundation under regular wave excitation. The numerical model was established and verified by OpenFOAM. The coupling mechanism of TLMCD and floating foundation was analyzed from the aspects of flow field, hydrodynamic loads, floating body motion and damping force. The results show that TLMCD has the best pitch suppression effect under resonant excitation, and that the liquid with a mass ratio of 2% reduces the maximum pitch response of the floating body under resonant excitation by 10.84% to 18.53%, and achieves at least 7.32% damping effect in the range of 0.9<T/T0<1.1. By numerical method, it was observed that under the condition of resonance, the hydrodynamic force generated by tank sloshing took up 89.52% of the time to do positive work, and that the sloshing of liquid in the liquid columns periodically provided reverse damping moment for the floating body.

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建立调谐多液柱阻尼器（TLMCD）与浮式基础的缩尺模型，在水池内开展试验，研究规则波激励下TLMCD对浮式基础纵摇运动响应的控制效果；同时利用OpenFOAM建立数值模型并进行验证，从流场、水动力载荷、浮体运动姿态和阻尼力做功等方面，分析TLMCD与浮式基础耦合的作用机理。结果表明：TLMCD在共振激励下的减摇效果最佳，2%质量比的液体可以降低浮体在共振激励下最大纵摇响应的10.84%~18.53%，在0.9<T/T0<1.1范围内TLMCD能实现至少7.32%以上的减摇效果；共振条件下液舱晃荡产生的水动力做正功的时间占比为89.52%，液柱内液体的晃荡周期性为浮体提供反向的阻尼力矩。

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通讯作者，E-mail：
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窦朋（1992-），男，博士，讲师

王志东（1968-），男，博士，教授，通讯作者，E-mail：。

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窦朋（1992-），男，博士，讲师

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窦朋（1992-），男，博士，讲师

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王志东（1968-），男，博士，教授，通讯作者，E-mail：。

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王志东（1968-），男，博士，教授，通讯作者，E-mail：。

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Main dimensions of the floating foundation model

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几何参数L1L2L3D1D2D3H1KG
实尺模型/m6.032.050.06.512.024.020.09.74
缩尺模型/mm41.25220.0343.7544.790160.0135.083.74
), ArticleFig(id=1242150731768210157, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150713795616870, language=CN, label=表1, caption=

浮式基础试验模型主尺度

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几何参数L1L2L3D1D2D3H1KG
实尺模型/m6.032.050.06.512.024.020.09.74
缩尺模型/mm41.25220.0343.7544.790160.0135.083.74
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Parameters of TLMCD for tests

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Av/m2Ah/m2Lv/mLh/mT0/sRfRm
0.000350.00007850.0450.39691.951.002.0
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TLMCD试验模型参数

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Av/m2Ah/m2Lv/mLh/mT0/sRfRm
0.000350.00007850.0450.39691.951.002.0
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Experimental conditions of TLMCD with floating

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F11.360.7
F21.560.8
F31.750.9
F41.951.04.6612.00.025, 0.038
F52.141.1
F62.341.2
F72.531.3
F81.360.7
F91.560.8
F101.750.9
F111.951.04.756无TLMCD0.025, 0.038
F122.141.1
F132.341.2
F142.531.3
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TLMCD与浮体作用试验工况

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工况T/sT/T0mFloating/kgRm（%）h/m
F11.360.7
F21.560.8
F31.750.9
F41.951.04.6612.00.025, 0.038
F52.141.1
F62.341.2
F72.531.3
F81.360.7
F91.560.8
F101.750.9
F111.951.04.756无TLMCD0.025, 0.038
F122.141.1
F132.341.2
F142.531.3
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Hydrodynamic moment of TLMCD

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T/T0Mx阻尼力矩节点激励力矩节点阻尼时间占比（%）阻尼力矩值/（N·m）激励力矩值/（N·m）阻尼力矩占比（%）
0.8945762.251.46E+086.48E+0769.29
0.91183378.155.17E+086.40E+0788.98
0.95MTLMCD1401192.727.54E+081.86E+0797.59
1.01401192.726.74E+081.35E+0798.03
1.051153676.167.57E+081.06E+0887.71
1.11836573.797.90E+081.88E+0880.78
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TLMCD 水动力力矩

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T/T0Mx阻尼力矩节点激励力矩节点阻尼时间占比（%）阻尼力矩值/（N·m）激励力矩值/（N·m）阻尼力矩占比（%）
0.8945762.251.46E+086.48E+0769.29
0.91183378.155.17E+086.40E+0788.98
0.95MTLMCD1401192.727.54E+081.86E+0797.59
1.01401192.726.74E+081.35E+0798.03
1.051153676.167.57E+081.06E+0887.71
1.11836573.797.90E+081.88E+0880.78
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调谐多液柱阻尼器对浮式风机基础的减摇特性研究
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窦朋 a , 王志东 a , 凌宏杰 b , 徐晓森 b
船舶力学 | 流体力学 2024,28(4): 513-526
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船舶力学 | 流体力学 2024, 28(4): 513-526
调谐多液柱阻尼器对浮式风机基础的减摇特性研究
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窦朋a, 王志东a , 凌宏杰b, 徐晓森b
作者信息
  • a.江苏科技大学　船舶与海洋工程学院，江苏　镇江　212003
  • b.江苏科技大学　海洋装备研究院，江苏　镇江　212003

    • 窦朋（1992-），男，博士，讲师

    王志东（1968-），男，博士，教授，通讯作者，E-mail：。

通讯作者:

通讯作者，E-mail：
Pitch mitigation characteristics of floating offshore wind turbine substructures with tuned liquid multi-column damper (TLMCD)
Peng DOUa, Zhi-dong WANGa , Hong-jie LINGb, Xiao-sen XUb
Affiliations
  • a.School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China
  • b.Marine Equipment and Technology Institute, Jiangsu University of Science and Technology, Zhenjiang 212003, China
出版时间: 2024-04-20 doi: 10.3969/j.issn.1007-7294.2024.04.004
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摘要
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建立调谐多液柱阻尼器（TLMCD）与浮式基础的缩尺模型，在水池内开展试验，研究规则波激励下TLMCD对浮式基础纵摇运动响应的控制效果；同时利用OpenFOAM建立数值模型并进行验证，从流场、水动力载荷、浮体运动姿态和阻尼力做功等方面，分析TLMCD与浮式基础耦合的作用机理。结果表明：TLMCD在共振激励下的减摇效果最佳，2%质量比的液体可以降低浮体在共振激励下最大纵摇响应的10.84%~18.53%，在0.9<T/T0<1.1范围内TLMCD能实现至少7.32%以上的减摇效果；共振条件下液舱晃荡产生的水动力做正功的时间占比为89.52%，液柱内液体的晃荡周期性为浮体提供反向的阻尼力矩。

TLMCD  /  浮式风机基础  /  模型试验  /  数值模拟

With a scale model of tuned liquid multi-column damper (TLMCD) and floating substructure established, experiments were carried out in a flume to study the control effect of TLMCD on the pitch motion response of the floating foundation under regular wave excitation. The numerical model was established and verified by OpenFOAM. The coupling mechanism of TLMCD and floating foundation was analyzed from the aspects of flow field, hydrodynamic loads, floating body motion and damping force. The results show that TLMCD has the best pitch suppression effect under resonant excitation, and that the liquid with a mass ratio of 2% reduces the maximum pitch response of the floating body under resonant excitation by 10.84% to 18.53%, and achieves at least 7.32% damping effect in the range of 0.9<T/T0<1.1. By numerical method, it was observed that under the condition of resonance, the hydrodynamic force generated by tank sloshing took up 89.52% of the time to do positive work, and that the sloshing of liquid in the liquid columns periodically provided reverse damping moment for the floating body.

TLMCD  /  floatingwind turbine substructure  /  model test  /  numerical simulation
窦朋, 王志东, 凌宏杰, 徐晓森. 调谐多液柱阻尼器对浮式风机基础的减摇特性研究. 船舶力学, 2024 , 28 (4) : 513 -526 . DOI: 10.3969/j.issn.1007-7294.2024.04.004
Peng DOU, Zhi-dong WANG, Hong-jie LING, Xiao-sen XU. Pitch mitigation characteristics of floating offshore wind turbine substructures with tuned liquid multi-column damper (TLMCD)[J]. Journal of Ship Mechanics, 2024 , 28 (4) : 513 -526 . DOI: 10.3969/j.issn.1007-7294.2024.04.004
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0　引言
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风力发电作为重要的可再生能源，将为我国实现“双碳”重大战略决策提供有力保障。海上风电靠近能源消耗中心且不占用土地资源，近年来发展迅猛。风机的安装方式呈现出由近海向深海、由固定式向浮式转变的趋势。深海风力资源更为丰富，但浮式风机的动力学特性也更为复杂，在风浪流载荷作用下，浮体的持续摆动会降低风机发电质量，影响风电机组的使用寿命，加剧平台疲劳损伤。因此，通过振动控制技术提升海上浮式风机的水动力性能，保障平台正常作业及系泊系统安全，已成为海上风电领域的重要研究课题。
调谐液体阻尼器TLD（Tuned Liquid Damper）是一种带有自由液面的水箱，可吸收结构运动所传递的能量并转化为流体运动，通过流体惯性将这部分能量反作用于结构以达到减摇抑振的效果，具有运维成本低、调频便捷和无需外部能量输入等优势，近年来得到了海上风电领域的广泛关注。Ha等[1]通过数值模拟研究发现，在Spar型浮式风机的顶部安装TLD可以提升浮式基础的纵摇控制效果。为了避免阻尼器自身质量对浮式基础带来的重心变化和基频漂移，阻尼器的质量一般选择为结构整体质量的1%~4%[2]。Zhang等[3]通过实时联动实验装置考虑了风力桨叶的受力情况，将晃荡力-风机摆动力考虑到结构运动方程中，求解结构实时运动响应，实现TLD与风机作用的全耦合实验模拟。
在TLD阻尼性能优化方面，Nguyen等[4]利用浅水波模型，提出了多个TLD系统（MTLD）的减振思路，同时利用Taguchi法进行系统优化，发现将TLD分解为多个浅水TLD可以在不改变质量比的前提下提升MTLD性能；Alkmim等[5]对调谐液柱阻尼器TLCD（Tuned Liquid Column Damper）进行优化使之能更好地应对随机风谱，发现不同的风廓线对优化结果有显著影响，即最佳TLCD参数依赖于风场模型；Altay等[6]在TLCD立柱壁面安装了可伸缩式舱壁，通过改变内舱壁截面积以控制阻尼器固有频率。
近年来，许多学者提出将TLD和调谐质量阻尼器TMD（Tuned Mass Damper）相结合。Xu等[7]将调谐质量块浸入TLD中，研究结构在自由衰减下的振动控制效果，结果表明，组合阻尼器振子在流场中往复运动耗散系统能量，提升了结构阻尼；Chen等[8]研究了用于控制结构振动的混合式TMD-TLD，该系统能有效地抑制共振频率附近剧烈的液体晃动，当质量比为11.2%、液体深度比为5/30时，最佳减振率可达70%；Love等[9]也提出了TMD和TLD耦合减振的单自由度控制模型，并获取了结构响应的非线性特征，发现耦合的阻尼减振装置对高层结构建筑有优异的阻尼特性，对结构固有频率变化具有鲁棒性；针对横风所致的风机振动控制问题，Sarkar等[10]将两个TLCD垂直排列，并通过磁流变设备以最大化耗能为目标优化了系统阻尼。
调谐多液柱阻尼器TLMCD（Tuned Liquid Multi-Column Damper）是传统TLD针对浮式风机结构在空间上进行的一种优化。Coudurier等[11]将其安装在浮式风机底部，通过建立浮体耦合运动理论方程发现，TLMCD控制浮体纵摇和横摇效果要优于传统的TLCD；Fath等[12]提出在TLMCD水平管道内布置螺旋桨驱动流体运动实现半主动化控制，并推导了等效力学模型；Hokmabady等[13]将TLMCD和调谐液柱气体阻尼器（TLCGD）相结合，组合后对规则波、不规则波和地震作用下结构响应的控制效果分别达到22%、60%和55%。
综上所述，TLMCD具有方向性好、阻尼性能强、稳定性高、启动快、无需能量输入等优势，在2018年首次被提出用于浮式风机的运动控制后便引起了众多学者的关注，但TLMCD对浮式风机阻尼的影响规律和耗能机制亟待深入研究。本文基于OpengFOAM建立TLMCD与浮式风机基础的耦合计算模型，并开展试验验证，研究波浪激励下TLMCD对浮式基础纵摇运动响应的控制效果，从流场、水动力载荷、浮体运动姿态和阻尼力做功等方面，分析TLMCD对浮式基础的减摇机制。研究成果可为提高海上浮式风机的运动控制技术奠定理论基础。
1　试验设置
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1.1　浮式基础模型
文中选取的浮体模型是OC4项目中的浮式风机基础，属于半潜式浮式平台，本文主要研究阻尼器对浮式基础部分的纵摇运动响应控制效果，因而未考虑风机和塔架结构的影响。模型试验在河海大学港口航道工程与海岸海洋科学实验中心进行，试验中造波水池宽1 m，平台模型的缩尺比设为1:144，图1给出了平台俯视图和正视图，表1给出了浮式基础的主尺度[14]。
1.2　TLMCD模型
图2给出了TLMCD的示意图，其固有频率可参照TLCD的固有频率进行设计，基于拉格朗日方程[15-16]假设：（1）流体是连续且不可压缩的；（2）液柱内部的自由表面是水平的；（3）阻尼器受到来自水平方向的振动，则两液柱内自由液面运动可表示为
式中，为TLMCD受到激励后水平x轴方向上的加速度，、和y分别为TLMCD液柱内液体的加速度、速度和位移，Av和Ah分别为“U”型管道垂向和水平管道的截面面积，ζ为阻尼比，ω0为阻尼器的固有频率，Le为TLMCD内液体的总长度，
式中，Lv和Lh分别为TLMCD内初始时刻垂向、水平液柱的长度。TLMCD的固有频率可表示为
式中，g为重力加速度。通过改变参数Av、Ah、Lv和Lh就可以改变TLMCD的固有频率，使之与浮体的纵摇固有频率相等。TLMCD的设计纵摇固有周期T0为1.95 s，具体参数见表2，其中Rf和Rm分别为TLMCD的调谐比和质量比。
1.3　模型和试验布置
图3为试验模型，平台主体由有机玻璃制成，TLMCD内的液体添加蓝色染色剂便于观察液位变化，波浪水池内空间有限，为避免缆绳拉力对平台纵摇周期造成影响，采用水平张紧式系泊，缆绳采用轻质软绳，用软弹簧对浮体运动实现缓冲。系泊点距离浮体足够远以保证浮体纵摇时弹簧对浮体的作用力较小，避免缆绳刚度影响整个耦合系统的纵摇固有频率，如图4所示。迎浪面单个缆绳长为1.880 m，预张力为0.6 N，刚度为80 N/m；背浪面两个缆绳长为3.955 m，预张力为0.3 N，刚度为80 N/m。波高选取0.025 m和0.038 m，对应五级和六级海况，波周期T取值范围为0.7<T/T0<1.3，对应涌浪的作用周期范围。浮体总质量为4.756 kg，通过改变浮体内液体压载的空间分布控制平台纵摇固有频率，最终重心高度（KG）为83.74 mm，三个自由度的转动惯量分别为Ixx=0.117 kg·m2，Iyy=0.117 kg·m2，Izz=0.197 kg·m2，TLMCD内液体质量占总质量的2%，即Km=2%。因此在考虑TLMCD作用的F1至F7组次中取出0.095 kg的配重铅沙，使吃水保持在135 mm，具体计算组次见表3，其中T为波浪周期，mFloating为浮体质量，h为波高。
2　数值方法
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2.1　控制方程
利用OpenFOAM开展数值仿真，采用InterDyMFoam两相流模型，该模型使用有限体积法对控制方程进行离散，将计算过程中涉及的物理量分为三种类型分别存储于控制体中心（速度、体积分数等）、控制体表面（界面通量φ等）、网格节点（网格位移等）。流体的控制方程为
式中，ϕ为通量，Γϕ为广义扩散系数，Sϕ为广义源项，ρ为流体密度，U为流体质点速度，从左往右依次为瞬时项、对流项、扩散项和源项。压力速度耦合采用PIMPLE算法，用VOF法捕捉自由表面，具体的求解步骤如图5所示。
2.2　浮体六自由度运动
模型中定义了两套不同的坐标系，如图6所示，一套坐标系为固定的全局坐标系O-XYZ，全局坐标系用于定义浮体坐标以及六自由度运动。另一套为中心固定于浮体重心处，随着浮体运动而运动的局部坐标系O'-X'Y'Z'。当浮体发生运动时，浮体的速度、加速度等矢量信息会在两套坐标系之间进行转换。
在固定的全局坐标系中，将六自由度运动模型中的六个自由度运动（纵荡、横荡、垂荡、纵摇、横摇、艏摇）分别表示为η =（η1，η2）=（x，y，z，φ，θ，ψ）。在随浮体运动的局部坐标系中，将沿局部坐标系的三个坐标轴的六个自由度运动分别表示为v =（v1，v2）=（u，v，w，p，q，r），前三个量表示浮体沿三个坐标轴的线速度，后三个量表示沿三个坐标轴转动的角速度。在全局坐标系下，对浮体位移求导则可以得到浮体速度矢量，对线位移η1求导则可以获得线速度，这个线速度与局部坐标系中的线速度v1之间可以通过转换矩阵J1互相转换，J1和互为逆矩阵：
角速度的转换也与线速度的类似，转换矩阵J2为
对浮体运动方程的建立主要基于牛顿第二定律，主要考虑浮体受到流场的力，包括物体表面的压力以及流体粘性剪切力，把浮体表面的单元作为研究对象，其面单元表示为σi，方向指向流场，与单元外法线方向相同。将单元所受流场作用力分解到两个方向上，沿单元表面法向的作用力分量FPi（该分量由流场内的压力引起）和沿单元表面切向的作用力分量FSi（该分量为流体粘性剪切力）。具体表示为式（8）和式（9），其中p表示该处的流场压力，τ表示流场切应力张量，i表示面单元编号：
此时将各个单元上的法向压力和切向剪切力进行积分求和，则可以得到浮体在流场中的整体受力。此外还需考虑浮体本身的重力，因此根据牛顿第二定律可得到浮体的线运动方程：
式中，m为浮体的质量，a为外载荷作用下浮体的线加速度，Fspr为系泊力。
浮体的转动方程为
式中，I代表转动惯量，αr代表转动角加速度，ri代表矢量半径，Mspr为系泊力矩。由于运动方程式是在局部坐标系下建立的，而方程中外力载荷的计算是在全局坐标系中计算的，所以需要通过矩阵J1和J2来进行坐标系间的转换。
2.3　数值造波和计算控制
本文中采用速度入口造波，深水Stocks波是水波最简单的解析解，其满足的色散方程为
用已知周期获得其波长L，该波理论的解基于势函数理论，从中可以得到自由面高程和速度场，对于沿X轴正方向传播的二维波，以一阶Stocks波为例，表达式为
式中，η为波面高程，k为波数，u、w分别为X轴方向和Z轴方向上的流体质点速度。
采用主动边界消波[17]，消波边界产生一个与入射方向相反的速度，沿着波浪高度的速度是恒定的，这与速度入口活塞造波方式相匹配，
式中，U是水平垂直积分（平均）速度，h为水深，c是波浪速度，η为自由表面高程。对于浅水波来说，速度满足
假设Uc为应用于垂直于边界并指向域的矢量校正速度，反射波高ηR为造波处的高程ηM与目标高程ηT相减，根据预期的反射自由波产生ηR = ηM - ηT，基于浅水理论，主动吸波的方程式为
流场的两侧和底部为壁面边界，顶部为大气压力，浮体六自由度不受约束，由多个线弹性缆进行控制，线弹性缆的预张力、位置和刚度与图4保持一致。
2.4　规则波作用下浮式基础与TLMCD耦合运动验证
根据1.1节中实验水池尺寸，建立的数值水池如图7所示，长度为18 m，宽度和高度都为1 m，全局坐标系的原点设在浮体重心位置。浮体和TLMCD尺寸见表1和表2。选取表3中F4工况的共振波浪激励条件，波高为0.025 m，计算域网格如图8所示，浮体及自由表面附近的网格逐层加密。
图9给出了共振波浪激励下浮体运动的时程曲线和图像对比，可以看到在浮体运动的前5秒内峰值存在一定误差，这可能是由前期波浪的实验和数值入射存在差异导致的，当波浪稳定后，纵摇响应的吻合度较高，平均峰值误差为1.81%。因此，基于OpenFOAM的数值方法可以有效模拟内、外流场和系泊力作用下的浮体运动。
3　结果与讨论
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3.1　波浪作用下TLMCD纵摇控制特性试验分析
图10给出了三个典型波浪周期下，不同波高时平台的纵摇时程曲线，T=1.56 s、1.95 s和2.34 s分别对应T/T0=0.8、1.0和1.2。可以观察到在TLMCD作用下，浮式平台的纵摇运动在整个时间段内都得到了控制，尤其是在T=1.95 s的浮体共振激励下其减摇效果明显，与TLMCD内液柱的自由衰减周期相同，液体晃荡为结构提供的水动力能最大程度地达到阻尼效果。偏离共振频率后，TLMCD与外激励周期失谐，阻尼效果下降。
当T/T0=1.0，h=0.038 m时，TLMCD对纵摇峰值的控制作用明显降低，图11给出了纵摇最大峰谷差ζφ（同个周期内纵摇峰谷差值最大）随激励周期和波高的变化规律，可以看到波浪周期达到浮体共振条件时的纵摇响应最大，h=0.025 m和0.038 m时最大峰谷值相差分别为26.15°和31.26°，在TLMCD作用下最大幅值分别降低了18.53%和10.84%。在0.9<T/T0<1.1范围内TLMCD能实现至少7.32%以上的减摇效果，但T/T0=0.7时效果分别降低至2.63%和2.96%。
图12~14给出了h=0.038 m，T/T0=0.8、1.0和1.2时耦合系统的运动响应视频截图，TLMCD内流体通过蓝色染色剂进行标识，浮体上方安装了倾角传感器，数据线保持松弛状态以降低对平台运动的影响。可以看到在短周期作用下，一个波浪周期内浮体的纵摇较小，TLMCD内液柱高度未发生明显变化，对浮体提供的水动力较低，同时由于失谐效应，迎浪面液柱1内的水柱几乎随平台抬艏而升高，艏倾降低，无法将水动力充分转化为阻尼力，因此该条件下的阻尼器减摇效果较差，最大纵摇幅值控制效果为5.83%。
当波浪周期达到1.95 s时（图13）浮体发生了剧烈运动，最大纵摇角为13.40°，液柱内的流体也发生了剧烈运动，在t=22.67 s时波浪到达平台首部，平台在波浪升力作用下发生抬艏运动，并在t=23.33 s时纵摇达到最大值，这个阶段内液柱1内的液位不断降低，为平台提供额外的恢复力矩。流体因自身惯性作用在t=23.67 s时继续向液柱2和液柱3内流动，为遭遇波谷阶段内的艏倾运动提供反向的恢复力矩，再次进入t=22.00 s时刻的状态不断循环往复。但在t=23.67 s的图中可以发现，因为浮体的纵摇量过大，导致空气进入了底部连通管道，降低了TLMCD的阻尼效果，这也是h=0.025 m的减摇率高于0.038 m时的原因。在图14的长周期波浪作用下，TLMCD内流体更容易流入相对高度低的一侧，可以观察到液柱的高度变化明显，所提供的水动力较大。
3.2　流场分布特征数值模拟
图15给出了TLMCD内的流速矢量图，可以清楚地看到内外流场的流速变化，图15（a）中波浪到达平台前端，抬艏运动使液柱1内液体的相对高度大于液柱2，压差力作用下液体向液柱2流动，由于立柱的半径大于底部连通管道，所以管道内的流速较大。结合图15中液柱1内液面变化与浮体运动角速度相位关系可以发现，t=7.6 s时液柱1内的液位到达最低点，此时的抬艏角速度达到峰值，加速度为零，意味着在t=6.2~7.6 s这个时间段内，通过液柱1内流体向下运动的过程，使平台前端获得了向下的作用力抑制抬艏运动，流体势能充分释放后平台的抬艏加速度正好降低至零点。
艏倾运动阶段中，液柱2和液柱3几何对称，都在7.6 s时获取了较大的势能储备，艏倾的加剧使得液柱2内的势能更大，管道内的流速逐渐降低并最终转向至液柱1（图15（c）），7.6~9.4 s的时间段内浮体保持艏倾运动，艏倾加速度在7.6~8.7 s内增加到最大值，并在9.4 s时艏倾加速度降低至零点，这个时间段内液柱2和3持续释放势能储备，使平台艉部产生向下的水动力用于抑制艏倾，同时赋予液柱1势能储备用于下个运动周期的运动控制。
水动力作用为浮式结构提供阻尼力矩从而起到减摇效果，液柱高度与浮体角速度的最佳延滞相位为π，如图16所示，ηc1和ωφ分别为液柱1内的液面波动高度和纵摇角速度，kl为缩尺比，该条件下液柱势能释放能充分起到阻尼作用，延滞相位偏差将使部分势能产生激励效果，波浪周期是引起相位偏差的主要原因，如图18所示。液舱晃荡和波浪载荷对浮体的转动体现在力矩上，图17给出了在共振波浪激励下TLMCD浮式平台所受水动力力矩的时程曲线，图中Mwave和MTLMCD分别为浮体外部波浪和内部晃荡所产生的水动力力矩。可以观察到，浮体除了外部结构受到波浪的力矩外，内部的液舱晃荡提供额外的力矩，但TLMCD的作用使得波浪力矩出现非线性作用，产生倍频信号成分，相比之下结构内壁面的晃荡载荷力矩波形较为稳定。
3.3　TLMCD的阻尼力矩特性数值分析
图18给出了TLMCD水动力为浮体提供阻尼力矩和激励力矩的时间节点值，以0.1 s为时间步长，红色正三角代表液舱晃荡在该时间节点内对浮式结构做正功，等效恢复力矩；蓝色倒三角则做负功，等效倾覆力矩。从图17中可以看到MTLMCD在10 s后趋于稳定，表4对10~25 s内水动力做正功和负功时间下的力矩积分，量化了TLMCD的阻尼时间占比和做功占比，可以直观地看到，当T/T0=1.0时液舱晃荡产生的水动力做正功的时间为22.2 s，占总时间的89.52%，图18中负功节点数量稀疏；T/T0=0.95时阻尼设备仍然保持88.71%的阻尼时间占比，但随着波浪周期偏离固有频率越远，TLMCD阻尼时间占比越低，T/T0=0.8和1.1时分别为66.94%和73.79%，在图18（a）和图18（f）中可以观察到正负做功的节点数趋近于对称分布。
从幅值上看长周期波浪增加了TLMCD的力矩值，但TLMCD减摇效果并不与力做功值相关联，非共振激励下的做正功占比随偏离固有周期程度的增大而降低，T/T0=0.8、1.0和1.1时，做正功占总值的71.97%、97.29%和82.63%。TLMCD可以有效降低浮式结构纵摇响应，初始时刻TLMCD通过浮体的转动形成液柱间压差，迫使流体在重力作用下流向低液位的液柱内，一个纵摇周期内流体通过浮体运动即可获足够的势能储备，浮体抬艏运动时，迎浪面液柱1内液体回落，与之对应的，浮体艏倾运动时，背浪面液柱2和液柱3内液体回落，通过势能转换达到抑制浮体运动的效果，当T/T0=1.0时TLMCD液柱高度与浮体角速度的延滞相位为π，此时晃荡载荷为浮体提供的力矩可最大程度地用于增加结构阻尼，T/T0偏离1.0时阻尼时间节点占比降低，对应激励节点占比提升。
4　结论
收起
为了研究TLMCD对浮式风机基础的减摇特性，本文建立TLMCD与浮式基础的缩尺试验模型，研究了规则波激励下TLMCD对浮式基础运动响应的控制效果，分析了波浪频率对TLMCD阻尼特性的影响规律；结合数值方法从流场、水动力载荷、浮体运动姿态和阻尼力做功等方面，分析了TLMCD与浮式基础耦合的作用机理。具体结论如下：
（1）2%质量比的TLMCD可以将浮体在共振激励下的最大纵摇响应降低10.84%~18.53%，并在0.9<T/T0<1.1范围内实现至少7.32%以上的减摇效果，具有进一步研究和推广的价值；
（2）基于OpenFOAM的数值方法可以有效模拟内、外流场和系泊力作用下的浮体运动，与模型试验结果的纵摇响应吻合度较高，稳态运动下平均峰值误差为1.81%；
（3）TLMCD通过液柱内的液体周期性运动吸收和释放机械能，晃荡水动力作用为浮式结构提供阻尼力矩，液柱高度与浮体角速度的最佳延滞相位差为π，延滞相位偏差将使部分机械能产生激励效果，波浪入射周期是引起相位偏差的主要原因；
（4）当T/T0=1.0时液舱晃荡产生的水动力做正功的时间占比为89.52%，但T/T0=0.8和1.1时降低至66.94%和73.79%，正负做功的节点数趋近于对称分布；
（5）TLMCD减摇效果并不与力做功值相关联，非共振激励下的做正功占比随偏离固有周期程度的增大而降低，T/T0=0.8、1.0和1.1时，做正功分别占总值的71.97%、97.29%和82.63%。
基金
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  • 国家自然科学基金资助项目(52171256; 52101314; 52301321)
  • 江苏省自然科学基金资助项目(BK20230669)
文献
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doi: 10.3969/j.issn.1007-7294.2024.04.004
  • 接收时间：2023-09-19
  • 首发时间：2026-03-21
  • 出版时间：2024-04-20
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  • 收稿日期：2023-09-19
基金
国家自然科学基金资助项目(52171256; 52101314; 52301321)
江苏省自然科学基金资助项目(BK20230669)
作者信息
    a.江苏科技大学　船舶与海洋工程学院，江苏　镇江　212003
    b.江苏科技大学　海洋装备研究院，江苏　镇江　212003

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