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Article(id=1243879753925640837, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243879752042398333, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2024.08.001, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1708272000000, receivedDateStr=2024-02-19, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774493643503, onlineDateStr=2026-03-26, pubDate=1724083200000, pubDateStr=2024-08-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774493643503, onlineIssueDateStr=2026-03-26, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774493643503, creator=13701087609, updateTime=1774493643503, 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=1133, endPage=1140, ext={EN=ArticleExt(id=1243879754168910475, articleId=1243879753925640837, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Surf-riding/broaching vulnerability criteria assessment method for waterjet propelled ships, columnId=1241023037940748650, journalTitle=Journal of Ship Mechanics, columnName=Hydrodynamics, runingTitle=null, highlight=null, articleAbstract=

The current Level 2 vulnerability criteria assessment method for the surf-riding/broaching stability failure mode of the IMO Second Generation Intact Stability Criteria only applies to ships using conventional propellers. However, waterjet propelled ships are also prone to this stability failure mode. Therefore, it is necessary to establish a regulatory assessment method for such a ship type as well. This study established a mechanical model for waterjet propulsion systems through the analogy to the model for propellers. The Level 2 vulnerability assessment method applicable to waterjet propelled ships was proposed and validated based on the actual pump data and sample ship calculations. A specific assessment method for waterjet propelled ships was proposed to overcome the limitation on propulsion type, which not only makes the regulation more complete, but also provides technical support for the stability safety assessment of waterjet propelled ships.

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当前国际海事组织（IMO）二代稳性规范中骑浪/横甩稳性失效模式的第二层薄弱性衡准校核方法仅适用于采用常规螺旋桨推进方式的船舶。然而，采用喷水推进方式的船舶同样属于该稳性失效模式的敏感船型，因此有必要建立此类船舶的规范校核方法。本研究通过类比螺旋桨推力模型，建立喷水推进系统的力学模型，在不改变当前骑浪/横甩第二层薄弱性衡准校核理论方法和框架的前提下，通过最少的流程变动实现适用于喷水推进船舶的第二层薄弱性衡准校核，并基于实泵数据和样船算例证明所提出方法的有效性。基于研究成果形成专门针对喷水推进船舶的规范校核方法，突破当前规范在船舶推进方式方面的局限性，不但使规范变得更为完备，而且能为喷水推进船舶的稳性安全评估提供有利的技术支撑。

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通讯作者，E-mail：
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封培元（1987-），男，博士，研究员，通讯作者，E-mail：

蔡佑林（1976-），男，博士，研究员

范佘明（1963-），男，博士，研究员。

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封培元（1987-），男，博士，研究员，通讯作者，E-mail：

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封培元（1987-），男，博士，研究员，通讯作者，E-mail：

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范佘明（1963-），男，博士，研究员。

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范佘明（1963-），男，博士，研究员。

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Thrust prediction error in percentage

, figureFileSmall=null, figureFileBig=null, tableContent=
额定转速百分比进流速度/（m∙s-1）
510152025
60%-0.070.02-0.22-0.161.29
80%-0.090.07-0.12-0.240.40
90%-0.100.07-0.10-0.250.17
100%-0.060.140.00-0.170.10
), ArticleFig(id=1243879767133503571, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243879753925640837, language=CN, label=表1, caption=

推力预报误差百分比

, figureFileSmall=null, figureFileBig=null, tableContent=
额定转速百分比进流速度/（m∙s-1）
510152025
60%-0.070.02-0.22-0.161.29
80%-0.090.07-0.12-0.240.40
90%-0.100.07-0.10-0.250.17
100%-0.060.140.00-0.170.10
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喷水推进船舶骑浪横甩薄弱性衡准校核方法
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封培元 1, 3 , 蔡佑林 1, 3 , 范佘明 2, 3
船舶力学 | 流体力学 2024,28(8): 1133-1140
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船舶力学 | 流体力学 2024, 28(8): 1133-1140
喷水推进船舶骑浪横甩薄弱性衡准校核方法
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封培元1, 3 , 蔡佑林1, 3, 范佘明2, 3
作者信息
  • 1.喷水推进技术重点实验室，上海　201100
  • 2.上海市船舶工程重点实验室，上海　200011
  • 3.中国船舶及海洋工程设计研究院，上海　200011

    • 封培元（1987-），男，博士，研究员，通讯作者，E-mail：

    蔡佑林（1976-），男，博士，研究员

    范佘明（1963-），男，博士，研究员。

通讯作者:

通讯作者，E-mail：
Surf-riding/broaching vulnerability criteria assessment method for waterjet propelled ships
Pei-yuan FENG1, 3 , You-lin CAI1, 3, She-ming FAN2, 3
Affiliations
  • 1.Science and Technology Laboratory on Waterjet Propulsion, Shanghai 201100, China
  • 2.Shanghai Key Laboratory on Ship Engineering, Shanghai 200011, China
  • 3.Marine Design and Research Institute of China, Shanghai 200011, China
出版时间: 2024-08-20 doi: 10.3969/j.issn.1007-7294.2024.08.001
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摘要
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当前国际海事组织（IMO）二代稳性规范中骑浪/横甩稳性失效模式的第二层薄弱性衡准校核方法仅适用于采用常规螺旋桨推进方式的船舶。然而，采用喷水推进方式的船舶同样属于该稳性失效模式的敏感船型，因此有必要建立此类船舶的规范校核方法。本研究通过类比螺旋桨推力模型，建立喷水推进系统的力学模型，在不改变当前骑浪/横甩第二层薄弱性衡准校核理论方法和框架的前提下，通过最少的流程变动实现适用于喷水推进船舶的第二层薄弱性衡准校核，并基于实泵数据和样船算例证明所提出方法的有效性。基于研究成果形成专门针对喷水推进船舶的规范校核方法，突破当前规范在船舶推进方式方面的局限性，不但使规范变得更为完备，而且能为喷水推进船舶的稳性安全评估提供有利的技术支撑。

二代稳性  /  骑浪/横甩  /  喷水推进  /  薄弱性衡准  /  校核流程

The current Level 2 vulnerability criteria assessment method for the surf-riding/broaching stability failure mode of the IMO Second Generation Intact Stability Criteria only applies to ships using conventional propellers. However, waterjet propelled ships are also prone to this stability failure mode. Therefore, it is necessary to establish a regulatory assessment method for such a ship type as well. This study established a mechanical model for waterjet propulsion systems through the analogy to the model for propellers. The Level 2 vulnerability assessment method applicable to waterjet propelled ships was proposed and validated based on the actual pump data and sample ship calculations. A specific assessment method for waterjet propelled ships was proposed to overcome the limitation on propulsion type, which not only makes the regulation more complete, but also provides technical support for the stability safety assessment of waterjet propelled ships.

second generation intact stability  /  surf-riding/broaching  /  waterjet propulsion  /  vulnerability criteria  /  assessment procedure
封培元, 蔡佑林, 范佘明. 喷水推进船舶骑浪横甩薄弱性衡准校核方法. 船舶力学, 2024 , 28 (8) : 1133 -1140 . DOI: 10.3969/j.issn.1007-7294.2024.08.001
Pei-yuan FENG, You-lin CAI, She-ming FAN. Surf-riding/broaching vulnerability criteria assessment method for waterjet propelled ships[J]. Journal of Ship Mechanics, 2024 , 28 (8) : 1133 -1140 . DOI: 10.3969/j.issn.1007-7294.2024.08.001
正文
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0　引言
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近年来，船舶因特殊稳性失效现象造成的海损事故时有发生，现行完整稳性规则对新船的适用性问题越来越引起业界关注。国际海事组织（IMO）为此从2009年起着手制定全新的船舶第二代完整稳性衡准规范（二代稳性）。经过十多年的反复论证，IMO最终在2020年12月颁布了MSC.1/Circ.1627通函[1]，正式通过了船舶第二代完整稳性规范的临时导则。该规范的主要目的是为五种全新的稳性失效模式提供安全性评估的手段，包括瘫船稳性、过度加速度、纯稳性丧失、参数横摇和骑浪/横甩。目前二代稳性临时导则已进入试用阶段，成员国被邀请试用这些衡准并反馈应用情况。通过收集试用经验，以供考虑是否有必要在未来进行修订。该试用期是修改和完善导则的最后时间窗口，强制执行后的船舶产品必须满足规范要求才能进入国际市场。
骑浪/横甩因其强非线性和混沌特质被认为是五种稳性失效模式中最为复杂的失效模式[2]。在随浪中高速航行的船舶突然失去航向保持能力并发生急速转向的现象被称为横甩。横甩时尽管使用了最大舵角却仍然不能维持预定的航向，并且伴有猛烈的艏摇，同时产生大角度横倾，直接危及舰船在波浪中的航行性能和安全[3]。而骑浪则是导致横甩的先决条件，航行实践和船模试验都表明骑浪是一种十分危险的状态，因此IMO在二代稳性中实际是针对骑浪现象进行规范校核。从力学上来分析，骑浪状态是纵向波浪力、推力和阻力在船速等于波速时达到动力平衡时的平衡态。预报骑浪运动的方法主要有解析方法[4]、模型试验方法[5]和数值仿真方法[6-7]。当前的骑浪/横甩第二层薄弱性衡准校核便是基于非线性动力学中的分叉理论，采用梅林科夫方法求解船舶发生骑浪的临界螺旋桨转速，以此为依据判断船舶是否存在发生骑浪的危险。
Feng等[8]、储纪龙等[9]对骑浪/横甩第二层薄弱性衡准规范进行了分析研究，明确了对衡准校核结果会产生影响的主要因素，包括波浪纵荡力、阻力曲线的拟合等；Begovic等[10]、Shin等[11]应用骑浪/横甩薄弱性衡准开展了大量的样船计算研究。然而，以上研究均仅针对采用螺旋桨推进方式的船舶。在IMO的SDC 3/WP.5文件[12]中指出了规范中缺少针对喷水推进、对转桨等推进方式船舶的规范校核方法，希望成员国能够提供解决方案。在SDC 7次会议上，中国基于文献[13]中的方法提交了一份提案，建议采用时域仿真的方法对喷水推进船舶的骑浪/横甩薄弱性进行校核，但由于方法并不成熟，未能在大会期间引起关注。然而，这并不意味着当前规范的这一局限性可被忽视。喷水推进因其具有高航速时推进效率高、抗汽蚀能力强、可在浅水环境中工作、能够提升船舶机动性和操纵性等优点，使得该技术在国际船舶市场，尤其是高性能船领域的应用日益广泛，是航速超过30 kn的水面船舶推进方式的首选。然而，中小型的高速船舶正是骑浪/横甩稳性失效模式的敏感船型，容易在随浪、艉随浪状态下发生骑浪/横甩现象。同时，为了配合喷水推进装置的安装，此类船舶的艉部侧投影面积一般较小，容易造成航向不稳定问题，加剧了船舶骑浪后进一步发生横甩的风险。因此，有必要针对喷水推进船舶的骑浪/横甩稳性安全建立相应的评估手段。
本研究通过类比螺旋桨推力模型，建立喷水推进系统的力学模型，在不改变当前骑浪/横甩第二层薄弱性衡准校核理论方法和框架的前提下，通过最少的流程变动实现适用于喷水推进船舶的第二层薄弱性衡准校核，并基于实泵数据和样船算例证明所提出方法的有效性。
1　骑浪/横甩第二层薄弱性衡准
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骑浪/横甩第二层薄弱性衡准适用于无法通过第一层薄弱性衡准的船舶，即船长大于200 m或傅汝德数高于0.3的船舶。
当船舶满足式（1）条件时，可认为其能够通过骑浪/横甩第二层薄弱性衡准要求：
式中，RSR=5×10-3为规范给出的标准值；C代表船舶发生骑浪的概率，由式（2）计算得到，其中W2为长期波浪统计数据中由有义波高HS和平均跨零周期TZ表征的不同海况的遭遇概率，Wij为对应不同波陡和波长规则波的概率权重，C2，ij表征船舶在规范指定的典型规则波工况中是否发生骑浪。
详细的骑浪/横甩第二层薄弱性衡准校核流程参见MSC.1/Circ.1627通函[1]，此处不再赘述公式细节，仅对整个校核流程进行概述。图1给出了骑浪/横甩第二层薄弱性衡准的校核流程，主要分为两个阶段：第一阶段为针对规范要求的不同波长λi和波高Hij组合的典型规则波工况，基于梅林科夫方法计算推进器的临界转速ncr，并由此得到C2，ij的值；第二阶段为针对长期波浪统计数据涵盖的不规则波海况，计算各个海况的权重系数W2及其相关联的规则波概率权重Wij，再通过式（2）计算得到骑浪发生概率C并通过式（1）判断船舶能否满足规范要求。
第二层薄弱性衡准校核所需的输入信息包括船舶的静水阻力数据、螺旋桨敞水推力数据、船体型值数据等。其中，敞水推力数据专门用于计算螺旋桨发出的推力：
式中，u为船舶的航速；n为螺旋桨的转速；tP为推力减额系数；ρ为流体密度；DP为螺旋桨直径；KT为推力系数，是表征螺旋桨敞水特性的关键参数，一般通过式（4）的多项式进行拟合近似：
其中，J为进速系数，是船舶航速u、伴流分数wP、螺旋桨转速n和直径DP的无因次函数：
其中，wP为伴流分数。
显然，对于喷水推进系统，上述的建模方式并不能直接套用。如何借鉴螺旋桨推进的力学模型建立适用于喷水推进的力学模型，并以此按照现有流程实现骑浪/横甩第二层薄弱性衡准的校核是本文研究关注的重点。
2　喷水推进力学建模
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由上述的衡准校核流程梳理可知，基于梅林科夫方法实现推进器临界转速的解析求解是骑浪/横甩第二层薄弱性衡准校核的关键所在。为使该方式能够进一步适用于喷水推进船舶，就需要根据喷水推进系统的力学原理建立类似螺旋桨推进方式的推力模型，其核心思想是引入类似螺旋桨力学模型中的推力系数来模拟喷水推进系统在不同进速和叶轮转速下的推力特性。
喷水推进系统推力建模的相关要素如图2所示。系统工作时，主机通过轴系带动叶轮旋转，水流以速度V0从进口吸入管道，推进泵叶轮再将机械能转化成水流的动能和压力能，最后经过导叶整流后到达喷口，以一定速度Vj喷离船尾。这股连续的水流所产生的反作用力即为喷水推进系统推动船舶前进的推力[14]。
由动量定理可知，喷水推进系统产生的推力等于其在单位时间内动量的增量。假设单位时间内通过推进泵的体积流量为Q，则喷水推进系统产生的总推力T[14]为
式中，α为船体边界层对进流动量的修正系数。
V0和Vj进一步需满足喷水推进系统的能量守恒关系[14]：
式中：H为推进泵的扬程；hc为水位提升高度（喷口中心线距水平面的高度）；kj为喷口损失系数；K1为流道损失系数；β为来流动能影响系数，反映了船体边界层对进流动能的影响程度。
推进泵的扬程与流量关系是表征其性能的关键要素，一般可通过水力试验获得。图3为某实泵在不同叶轮转速下的水力试验结果。从中可以发现，采用二次多项式拟合可以很好地近似推进泵的扬程和流量关系：
流量Q可通过泵的喷口面积Aj和喷射速度Vj计算得到：
联立式（7）~（9）便可求得任意进流速度V0情况下喷泵的喷射速度Vj，进而代入式（6）便可计算得到喷水推进系统产生的推力。
虽然基于上述力学模型能够实现推力计算，但无法直接适用于骑浪/横甩的薄弱性衡准校核。为此，借鉴螺旋桨的推力建模方法，引入喷水推进系统的推力系数：
式中，KWJ为喷水推进系统的推力系数，JWJ为式（11）定义的针对喷水推进方式的进速系数，nWJ为推进泵叶轮的转速，DWJ为叶轮直径。
进一步就如何获取式（10）中的系数开展研究。为获得KWJ~JWJ曲线的拟合关系，需要首先计算出一系列不同JWJ对应的KWJ值。由式（11）可知，可通过变化V0或变化nWJ的方式得到不同的JWJ。对于每个（V0，nWJ）组合，可通过所建立的力学模型计算得到喷水推进系统产生的推力T，进而可得对应的推力系数KWJ。
基于图3中的实泵数据，采用固定V0、变化nWJ方式得到的结果如图4所示。分别假定进流速度为5 m/s、10 m/s、15 m/s、20 m/s和25 m/s，配合60%、80%、90%和100%额定转速，共计得到20个数据点。将基于全部20个数据点的拟合结果与不同进流速度下的分组数据拟合结果进行对比可以发现：两种方式得到的拟合曲线几乎重合，但由于固定V0、变化nWJ方式得到的JWJ变化范围较小，采用分组拟合方式只能覆盖有限的范围，无法保障数据点外范围的KWJ~JWJ曲线拟合精度。
图5中相应给出了固定nWJ、变化V0方式得到的KWJ~JWJ曲线拟合结果。从中同样可以看到，基于全部20个数据点的拟合结果与不同叶轮转速下的分组数据拟合结果几乎重合。更为重要的是，对于某个固定的nWJ，通过变化一系列V0得到的JWJ数据点分布均匀，能够覆盖较广的范围，因此可以基于推进泵在某个特定叶轮转速下的扬程-流量关系计算得到KWJ~JWJ曲线的拟合关系式。
由KWJ~JWJ拟合关系可以非常快速地计算得到喷水推进系统产生的推力：
表1中定量给出了基于100%额定转速得到的KWJ~JWJ拟合关系按式（12）得到的喷水推进系统推力T和基于式（6）~（9）计算得到的准确结果T*之间的误差百分比，即（T-T*）/T*×100%，对应不同的进流速度和额定转速组合工况。从表中结果可以看出两者的最大误差为1.29%，且对应额定转速最低、进流速度最大的极端情况。
上述分析证明了基于式（10）计算喷水推进系统推力的有效性和精确性，采用该推力建模方式后可直接套用现有的骑浪/横甩第二层薄弱性衡准方法对喷水推进船舶进行校核，无需对现有衡准规范的流程进行任何改动。
3　样船计算
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下面以一艘四喷泵高速喷水推进船为例，具体阐述校核过程。目标船的船长L=95 m、航速VS=22 kn（对应傅汝德数Fn=0.37），因此不满足骑浪/横甩第一层薄弱性衡准要求，需要进行第二层衡准校核。
目标船的阻力数据如图6所示，按三次多项式对数据点进行拟合后得到阻力曲线的拟合系数。喷水推进系统的推进泵在额定转速下的扬程-流量测试及多项式拟合结果如图7所示。采用本文中提出的喷水推进系统推力建模方法，基于拟合得到的额定转速下推进泵扬程-流量多项式，进一步计算不同进流速度V0对应的JWJ和KWJ值，通过拟合得到式（10）中的系数k0、k1和k2。本目标船推力系数的拟合结果如图8所示，计算点对应的进流速度分别为0.5VS、0.75VS、VS、1.25VS、1.5VS和2VS，计算中用到的经验参数取值为：α=0.90，β=0.81，kj=0.03，K1=0.25。
基于以上输入数据，可采用与螺旋桨推进船舶完全相同的流程实现骑浪/横甩第二层薄弱性衡准校核，得到的骑浪发生临界曲线如图9所示。图中横坐标为波陡，纵坐标为波长-船长比，曲线右下侧区域为骑浪发生区域，即式（2）中C2，ij=1的点。从图中可知：目标船在λ/L=1~1.4范围内容易发生骑浪横甩，在规范考虑的整个波陡范围内C2，ij均为1；随着波长船长比的增加，船舶在小波陡中发生骑浪的概率逐渐降低。
目标船对应设计航速的衡准值计算结果为C=0.046，超出了规范标准值，因此无法通过第二层薄弱性衡准校核，说明目标船对于骑浪/横甩稳性失效模式是比较敏感的。进一步计算不同船舶航速对应的骑浪/横甩薄弱性衡准值可以得到如图10所示的衡准值C随傅汝德数Fr变化曲线，该曲线与标准值水平线的交点即为目标船能够满足规范要求的航速点。对本目标船而言，当Fr=0.322时能够满足规范要求，对应的降速比例约为13%，该结果可供船舶设计和营运参考。
4　结论
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本研究提出了一种基于推力系数的喷水推进系统推力建模方法，能够适用于国际海事组织的骑浪/横甩第二层薄弱性衡准校核，从而对喷水推进船舶的骑浪/横甩稳性失效风险进行有效的评估，有利于提升此类船舶的航行安全。研究得到的主要结论如下：
（1）基于实泵数据的验证结果表明文中所提出的推力模型是精确有效的，即喷水推进系统的推力也可按照类似螺旋桨的方式进行模拟；
（2）所提出的推力模型可直接用于喷水推进船舶的骑浪/横甩第二层薄弱性衡准校核，无需对规范流程进行任何变动；
（3）针对目标船的计算校核结果表明该船是骑浪/横甩稳性失效模式的敏感船型，设计航速下的衡准值无法满足衡准要求，需降速约13%方可通过。
后续研究将进一步关注喷水推进船舶的第三层直接稳性评估方法，从而形成完整的面向喷水推进船舶的骑浪/横甩稳性评估方法体系。
基金
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  • 国家自然科学基金资助项目(51709240)
文献
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参考文献 引证文献
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2024年第28卷第8期
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doi: 10.3969/j.issn.1007-7294.2024.08.001
  • 接收时间：2024-02-19
  • 首发时间：2026-03-26
  • 出版时间：2024-08-20
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  • 收稿日期：2024-02-19
基金
国家自然科学基金资助项目(51709240)
作者信息
    1.喷水推进技术重点实验室，上海　201100
    2.上海市船舶工程重点实验室，上海　200011
    3.中国船舶及海洋工程设计研究院，上海　200011

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2种不同金属材料的力学参数
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
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