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Article(id=1243253929547514507, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243253924128469739, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2025.07.003, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1737475200000, receivedDateStr=2025-01-22, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774344435345, onlineDateStr=2026-03-24, pubDate=1752940800000, pubDateStr=2025-07-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774344435345, onlineIssueDateStr=2026-03-24, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774344435345, creator=13701087609, updateTime=1774344435345, updator=13701087609, issue=Issue{id=1243253924128469739, tenantId=1146029695717560320, journalId=1240685776644648972, year='2025', volume='29', issue='7', pageStart='1013', pageEnd='1180', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774344434053, creator=13701087609, updateTime=1774501521460, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1243912796535107926, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243253924128469739, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1243912796535107927, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243253924128469739, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1034, endPage=1047, ext={EN=ArticleExt(id=1243253929832727190, articleId=1243253929547514507, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Numerical simulation study on turning maneuverability of a ship in arctic region with pack ice, columnId=1241023037940748650, journalTitle=Journal of Ship Mechanics, columnName=Hydrodynamics, runingTitle=null, highlight=null, articleAbstract=

To investigate the turning maneuverability of polar ships in floating ice area, in this study a combined CFD-DEM approach was adopted to numerically simulate the turning motion process of a medium-sized polar ship in floating ice area. In the simulation the ship’s turning motion at different rudder angles and ice concentrations have been considered, and the parameters of the ship’s turning motion have been predicted. The results show that the existence of floating ice will significantly hinder the ship’s turning motion, and the range of the tactical diameter in floating ice area is 1 to 1.5 times than that in open water conditions. The forces and moments acting on the hull exhibit strong randomness, and the instantaneous fluctuations of the ship’s speed and yaw rate are more pronounced. At the same rudder angle, the ice longitudinal force increases with the increase of ice concentration, while the variation of the fluid longitudinal force is not significant. The average total lateral force and total yawing moment are in the same direction as the turning maneuver, while the average ice yawing moment tends to be in the opposite direction.

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为探究极地船舶在极地浮冰区中的回转操纵特性，本文采用CFD-DEM相结合的方法，针对一艘中型极地船舶在浮冰区中的回转运动过程进行了数值仿真研究。模拟考虑了船舶在不同舵角以及不同密集度浮冰区中的回转过程，并对船舶回转运动的参数进行预报。结果表明，浮冰的存在会对船舶的回转运动产生显著阻碍，浮冰区回转战术直径的范围是敞水工况战术直径的1~1.5倍。船体受到的力和力矩具有较强的随机性，航速与艏摇角速度时历曲线瞬时起伏更明显。相同舵角下，船舶受到的冰纵向力随浮冰密集度增加而增加，流体纵向力变化不明显；平均总侧向力、总偏航力矩方向与回转操纵方向一致，平均冰偏航力矩则更多偏向于回转操纵的相反方向。

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闫宏生（1973-），男，博士，副教授，E-mail：

陈梓昊（1998-），男，硕士研究生。

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闫宏生（1973-），男，博士，副教授，E-mail：

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闫宏生（1973-），男，博士，副教授，E-mail：

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陈梓昊（1998-），男，硕士研究生。

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陈梓昊（1998-），男，硕士研究生。

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ArticleFig(id=1243253945112576402, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253929547514507, language=EN, label=Tab.1, caption=

Principal dimensions of the ship

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名称/单位数值
船长/m104.4000
船宽/m18.4000
型深/m8.5000
设计吃水/m5.5500
设计方形系数0.6136
设计排水量/t6646.0000
), ArticleFig(id=1243253945209045398, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253929547514507, language=CN, label=表1, caption=

船舶设计主尺度

, figureFileSmall=null, figureFileBig=null, tableContent=
名称/单位数值
船长/m104.4000
船宽/m18.4000
型深/m8.5000
设计吃水/m5.5500
设计方形系数0.6136
设计排水量/t6646.0000
), ArticleFig(id=1243253945301320088, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253929547514507, language=EN, label=Tab.2, caption=

Geometric parameters of the rudder

, figureFileSmall=null, figureFileBig=null, tableContent=
名称/单位数值
舵展长/m4.70
叶根弦长/m5.00
叶尖弦长/m4.00
舵叶根厚度/m0.62
舵叶尖厚度/m0.40
后掠角/(°)5.41
), ArticleFig(id=1243253945389400475, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253929547514507, language=CN, label=表2, caption=

舵叶的几何参数

, figureFileSmall=null, figureFileBig=null, tableContent=
名称/单位数值
舵展长/m4.70
叶根弦长/m5.00
叶尖弦长/m4.00
舵叶根厚度/m0.62
舵叶尖厚度/m0.40
后掠角/(°)5.41
), ArticleFig(id=1243253945452315038, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253929547514507, language=EN, label=Tab.3, caption=

Geometric parameters of the rudder

, figureFileSmall=null, figureFileBig=null, tableContent=
名称/单位数值
内半径/m0.545
外半径/m2.450
厚度/m0.254
流入平面半径/m2.500
流入平面偏移/m0.500
螺旋桨旋向右旋
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虚拟盘体参数

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名称/单位数值
内半径/m0.545
外半径/m2.450
厚度/m0.254
流入平面半径/m2.500
流入平面偏移/m0.500
螺旋桨旋向右旋
), ArticleFig(id=1243253945599115687, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253929547514507, language=EN, label=Tab.4, caption=

Simulation method and parameters of interphase interactions

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相互作用类型启用模型系数值
静摩擦系数：0.05
冰-冰Hertz-Mindlin法向复原系数：0.2
切向复原系数：0.2
静摩擦系数：0.05
冰-船体壁面Hertz-Mindlin法向复原系数：0.5
切向复原系数：0.5
冰-海水VOF-Lagrange
冰-空气VOF-Lagrange
), ArticleFig(id=1243253945687196074, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253929547514507, language=CN, label=表4, caption=

相间相互作用

, figureFileSmall=null, figureFileBig=null, tableContent=
相互作用类型启用模型系数值
静摩擦系数：0.05
冰-冰Hertz-Mindlin法向复原系数：0.2
切向复原系数：0.2
静摩擦系数：0.05
冰-船体壁面Hertz-Mindlin法向复原系数：0.5
切向复原系数：0.5
冰-海水VOF-Lagrange
冰-空气VOF-Lagrange
), ArticleFig(id=1243253945775276462, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253929547514507, language=EN, label=Tab.5, caption=

Mean values of ice resistance from experimental and numerical results

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浮冰密集度船模实验值/N数值实验值/N误差
0.54.444.562.7%
0.75.074.981.8%
0.95.345.492.8%
), ArticleFig(id=1243253945913688502, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253929547514507, language=CN, label=表5, caption=

船模实验与数值实验的冰阻力均值

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浮冰密集度船模实验值/N数值实验值/N误差
0.54.444.562.7%
0.75.074.981.8%
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极地浮冰区船舶回转操纵性数值仿真研究
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闫宏生 1 , 陈梓昊 1 , 王锡军 2
船舶力学 | 流体力学 2025,29(7): 1034-1047
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船舶力学 | 流体力学 2025, 29(7): 1034-1047
极地浮冰区船舶回转操纵性数值仿真研究
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闫宏生1 , 陈梓昊1, 王锡军2
作者信息
  • 1.天津大学　建筑工程学院，天津　300072
  • 2.国家管网西南管道公司输油气分公司，南宁　530200

    • 闫宏生（1973-），男，博士，副教授，E-mail：

    陈梓昊（1998-），男，硕士研究生。

Numerical simulation study on turning maneuverability of a ship in arctic region with pack ice
Hong-sheng YAN1 , Zi-hao CHEN1, Xi-jun WANG2
Affiliations
  • 1.School of Civil Engineering, Tianjin University, Tianjin 300072, China
  • 2.PetroChina Company Limited Southwest Branch, Nanning 530200, China
出版时间: 2025-07-20 doi: 10.3969/j.issn.1007-7294.2025.07.003
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摘要
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为探究极地船舶在极地浮冰区中的回转操纵特性，本文采用CFD-DEM相结合的方法，针对一艘中型极地船舶在浮冰区中的回转运动过程进行了数值仿真研究。模拟考虑了船舶在不同舵角以及不同密集度浮冰区中的回转过程，并对船舶回转运动的参数进行预报。结果表明，浮冰的存在会对船舶的回转运动产生显著阻碍，浮冰区回转战术直径的范围是敞水工况战术直径的1~1.5倍。船体受到的力和力矩具有较强的随机性，航速与艏摇角速度时历曲线瞬时起伏更明显。相同舵角下，船舶受到的冰纵向力随浮冰密集度增加而增加，流体纵向力变化不明显；平均总侧向力、总偏航力矩方向与回转操纵方向一致，平均冰偏航力矩则更多偏向于回转操纵的相反方向。

极地船舶  /  离散元方法  /  计算流体力学  /  浮冰区  /  操纵性

To investigate the turning maneuverability of polar ships in floating ice area, in this study a combined CFD-DEM approach was adopted to numerically simulate the turning motion process of a medium-sized polar ship in floating ice area. In the simulation the ship’s turning motion at different rudder angles and ice concentrations have been considered, and the parameters of the ship’s turning motion have been predicted. The results show that the existence of floating ice will significantly hinder the ship’s turning motion, and the range of the tactical diameter in floating ice area is 1 to 1.5 times than that in open water conditions. The forces and moments acting on the hull exhibit strong randomness, and the instantaneous fluctuations of the ship’s speed and yaw rate are more pronounced. At the same rudder angle, the ice longitudinal force increases with the increase of ice concentration, while the variation of the fluid longitudinal force is not significant. The average total lateral force and total yawing moment are in the same direction as the turning maneuver, while the average ice yawing moment tends to be in the opposite direction.

polar ship  /  discrete element method  /  computational fluid dynamics  /  pack ice zone  /  maneuverability
闫宏生, 陈梓昊, 王锡军. 极地浮冰区船舶回转操纵性数值仿真研究. 船舶力学, 2025 , 29 (7) : 1034 -1047 . DOI: 10.3969/j.issn.1007-7294.2025.07.003
Hong-sheng YAN, Zi-hao CHEN, Xi-jun WANG. Numerical simulation study on turning maneuverability of a ship in arctic region with pack ice[J]. Journal of Ship Mechanics, 2025 , 29 (7) : 1034 -1047 . DOI: 10.3969/j.issn.1007-7294.2025.07.003
正文
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0　引言
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随着北极地区的冰川融化和航运活动增加，冰区船舶操纵性研究的重要性越来越突出。与开阔水域相比，浮冰区具有更复杂的环境条件。海冰的存在涉及到船舶与冰之间的相互作用，对船舶的操纵性能提出了独特的要求，需要研究船舶在冰区的航行特性和操纵策略[1]。因此，为保障船舶安全和提高航行效率，必然要求冰区船舶具有良好的冰区操纵性。
对于船舶在静水及波浪中操纵性能的研究，许多研究人员通过确定水动力导数和利用MMG操纵性方程[2]来实现对船舶操纵性能的预报[3-5]。MMG方法的准确度直接依赖于方程中水动力导数的精度，相关水动力导数需要通过经验公式、实验或数值模拟获得。另一方面，部分学者采用CFD方法直接对船舶的操纵过程进行模拟，并且在模拟结果中体现了CFD方法的优势[6-8]。此外，何涛[9]、操戈[10]、Shang H等[11]的研究表明，利用重叠网格法以及体积力法对计算模型进行简化，在操纵运动的模拟中依然可以取得较高的精度。CFD方法在一定程度上避免了建立数学模型和确定水动力导数时所做的简化和假设，并且考虑了流体的粘性，能更加直观地对操纵性进行预测，但是需要消耗大量的计算资源。
船舶在冰区中航行的操纵性比在开放水域中更复杂，除了船与水之间的相互作用，还涉及船与冰之间的相互作用。对于船-冰的相互作用、冰阻力预报等问题，国际上已经进行了较多研究。实验[12-13]与数值模拟[14-15]研究均表明，船体阻力、船冰作用模式与航速、浮冰密集度等因素密切相关。在数值模拟的研究中，DEM方法可以很好地对具有离散特性的浮、碎冰进行建模分析，在计算浮冰之间以及浮冰与船体之间的作用力方面具有独特优势；通过CFD和DEM方法的耦合，可以很好地模拟船体-水-浮冰之间的相互作用。
然而，大部分有关冰区船舶性能的研究都集中在快速性能上，对冰区操纵性能的研究则相对较少，Lau[16]、Su[17]等曾对平整冰航行工况下船舶回转运动进行了研究。对于普通冰区船舶来说，会尽可能避免与较厚的平整冰或大体积浮冰相撞，因此普通冰区船舶与海冰接触的模型不应与破冰船模型相同。针对浮冰区工况，王超等[18-19]通过经验公式确定冰阻力，以外力项代入MMG模型预测冰区船舶回转运动，确定浮冰工况下斜航运动的水动力导数，结合MMG模型预测冰区船舶回转运动。由于该方法准确性受经验公式和假设条件的限制，且得出冰、水耦合后水动力导数随机性较大，因此直接利用MMG模型并不能很好地反映浮冰对船舶航行的影响。Zhan等[20-21]把基于MMG模型的操纵预报代码SML和DEM方法相结合，模拟了浮冰条件下船舶的操纵运动，其模拟结果与实验结果较为吻合。狄少丞等[22]基于船舶六自由度操纵运动方程结合DEM方法，对“雪龙”船在平整冰区与浮冰区的回转过程以及特性进行了模拟和分析。
基于上述研究，本文采用CFD-DEM相结合的方法，对一艘中型极地船舶进行浮冰区回转性能的数值仿真研究，通过在不同舵角状态下以及不同密集度的浮冰区内的回转性能分析，对船舶在浮冰区的操纵性能进行预报。
1　理论基础
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1.1　CFD方法
CFD方法的基本原理是通过联立边界条件，从而对控制流体的连续性方程以及动量守恒方程进行求解。在实际应用中，流体域的解通过求解雷诺平均纳维尔-斯托克斯（RANS）方程获得，方程如下：
式中，ui是时均速度，Fi是体积力的合力，是速度波动，ρ是流体密度，是时均压力，μ是流体的运动粘度系数，是雷诺应力项。
RANS方法求解流体控制方程时考虑流体的粘性，需要引入湍流模型使方程组封闭，本文采用的湍流模型为SST（剪切应力传输）k-ω模型，其封闭方程为
式中，k是湍流动能，ω是单位耗散率，Gk是平均速度梯度产生的湍动能，Gω是计算ω的方程，Γk、Γω分别是k和ω的扩散率，Yk、Yω是湍流扩散项，Dk是交叉扩散项，Sk、Sω是源项。
1.2　DEM方法
将浮冰离散成DEM颗粒，其运动可认为是平移与旋转的组合，并满足下列运动方程：
式中，mi为单元i的质量，vi为其形心处的速度矢量，表示单元i与单元j之间的接触力，为单元所受到的其他合外力，bi为单元自身的体积力。Ii为单元i的转动惯量，ωi为其角速度矢量，表示单元i、j之间的切向接触力，rij表示两单元接触的作用点到单元i形心之间的距离，为旋转弹簧产生的力矩，为单元i受到的其他外力矩。
在离散元方法的计算中，假定球形颗粒为刚体且不会变形。两个单元之间的接触力Fc在接触点上可分解为法向力Fn和切向力Ft，并分别由一组弹簧-阻尼器模型进行表示。在弹簧-阻尼器模型中，弹簧表征响应的弹性部分，产生弹性恢复力；阻尼器表征碰撞期间的能量耗散，产生粘性阻尼力。
对于法向力Fn，有下式成立：
式中，Kn为法向弹簧刚度，Nn为法向阻尼，dn为接触点处法向上的重叠量，vn为接触点处相对球体表面速度的法向速度分量。
对于切向力Ft则有：
式中，Kt为切向弹簧刚度，Nt为切向阻尼，dt为接触点处切向上的重叠量，vt为接触点处相对球体表面速度的切向速度分量，Cfs为静摩擦系数。
2　计算模型
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2.1　船体几何模型及坐标系
本文以某中型极地船舶为对象，采用STAR-CCM+软件，对其在浮冰区的回转运动进行数值仿真研究。船舶主尺度及舵叶的几何参数分别如表1、表2所示。模拟过程中采用两套坐标系描述六自由度船体的回转运动，分别为固定坐标系O0-x0y0z0以及随船坐标系O-xyz，如图1所示。固定坐标系的原点固定在一特定点上，不允许平移和旋转运动，主要用于描述船体的运动轨迹；随船坐标系的原点固定在船舶质心上，并随船体的六自由度运动进行平移与旋转，主要用于描述船舶速度、受到的力及力矩等物理量。
2.2　计算域设定
一般情况下，对船舶回转操纵的模拟需要构建一个能容纳完整回转圈的计算域，但这种建模方法构建的计算域过大，计算时间很长。为提高计算效率，本文采用移动计算域[23]的方法构建计算域，即设定远场计算域在纵荡、横荡、艏摇三自由度上与船体模型的运动保持同步，并在此基础上对远场计算域进行单次网格划分和局部加密。这种建模方法可有效减少计算域网格数，大幅缩减计算时间。
考虑船舶主尺度、船体兴波以及浮冰区域等因素，构建的远场计算域尺寸如下：计算域的长和宽均为4倍船长，船上方远场计算域高度为1倍船长，船下方计算域高度为2倍船长。自由表面的位置根据船体的吃水值设置，计算域分为流体域（水）和空气域，其边界类型如图2所示。自由表面采用流体域体积（VOF）法[24]进行建模，并设定水和空气的密度和粘度分别为ρwater=997.56 kg/m3，ρair=1.18 kg/m3，μwater=8.89×10−4 Pa⋅s，μair=1.86×10−4 Pa⋅s，采用有限体积法对流体区域的控制方程进行离散和求解。
采用重叠网格方法[25]在船体几何模型周围构建近场计算域。在壁面或边界附近生成棱柱层网格，以期精确求解近壁流动；同时对部分关键区域进行网格加密，如船体模型的近场域、舵体、船尾兴波区域以及自由表面。模型的总网格数约为250万，生成的网格布局如图3所示。船体运动采用动态流体固体相互作用（DFBI）模型进行模拟，即把船舶几何模型的体表面包含区域设置成三维连续体，允许船体在六自由度上自由运动。螺旋桨的控制力通过体积力法模拟，即在船体模型的舵前部添加圆柱形的虚拟盘体模拟螺旋桨，同时在RANS方程的右端添加体积力项fbi模拟螺旋桨产生的推力和扭矩，进而实现船舶自航模拟。虚拟盘体模型参数如表3所示。
2.3　浮冰DEM模型
极地浮冰由于形成条件的不同而导致其形态各异，其中存在尺寸相对较大的不规则浮冰块，如图4（a）所示。与平整冰碎裂而成的浮冰不同，浮冰块与船舶的作用模式以推离、堆积为主，破碎较少。根据有关监测数据，北极航道浮冰的一般特征尺寸为0.5~8 m左右[26]。本文采用对数正态函数描述不同尺寸浮冰数量的分布[15，27]，浮冰的最小尺寸为2 m，最大尺寸为8 m，平均尺寸为5 m。基于拉格朗日多相模块构建浮冰DEM颗粒模型，密度取为ρice=916.72 kg/m3。参考浮冰块的形状，采用球形颗粒构成不规则棱柱体模拟单个浮冰块，生成的浮冰块模型如图4（b）所示。
将浮冰建模为DEM颗粒后，计算过程中会出现冰-冰、冰-船体壁面、冰-水、冰-空气4种相互作用类型。对于冰-冰和冰-船体壁面之间的碰撞，采用Hertz-Mindlin接触模型[28]进行描述。Zhang等[29]针对Hertz-Mindlin（HM）、线性弹簧（LS）和Walton-Braun（WB）三种接触模型对船舶与冰的碰撞进行了模拟，并与试验结果进行比较发现，三种接触模型在冰阻力计算差异不明显，且Hertz-Mindlin接触模型的相对误差最小。HM模型是一种非线性接触模型，其使用实时重叠位移计算接触力，考虑了弹性变形和滑移效应，可更准确地模拟船与冰之间的接触。为减少计算时间，冰-水、冰-空气的相互作用采用单向耦合机制，即将CFD计算的流体流场导出，作为外力作用于DEM冰颗粒，忽略冰粒子对流场的影响。相间的相互作用模型系数如表4所示。
计算中采用喷射器喷射离散元颗粒的方式在计算域内生成浮冰场，把喷射器输入到具有一定横纵分辨率的显示网格中，迭代一段时间，便可在指定区域生成浮冰。显示网格是在某一划定的平面范围内以指定的横纵分辨率均匀地分布探针，其作用是对接喷射器位置。通过调整显示网格的分辨率，可实现生成不同浮冰分布密集度的浮冰场。
3　模拟结果分析与讨论
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3.1　模型实验验证
由于国内实验条件的不足，难以进行冰区操纵性实验，因此针对船舶冰区航行操纵性能的研究仍以仿真为主。为验证数值模型的适用性，本文先使用根据一定缩尺比进行缩小的船体模型进行了浮冰区直航阻力的数值仿真，同时与实际船模的浮冰区直航阻力实验数据进行对比。通过二者结果的对比，在检验了数值模型用于反映船体所受冰力特性的适用性后，再使用相同参数设置的实船数值模型进行操纵性的仿真。
船模与实船的几何缩尺比为1:20，实验用船体模型如图5所示；同时在数值建模过程中，浮冰颗粒尺寸也根据1:20的缩尺比进行缩小。模型实验与数值实验均在航速0.575 m/s（实船航速5 kn）的条件下进行，图6-7为模型实验的实验场景，其冰阻力均值结果如表5所示。目前国内外研究船、冰作用力时，采用平均值表征船所受冰力的大小[30]，因此冰阻力均值对于验证本数值模型的适用性具有较强的参考意义。由结果对比可知，二者具有较好的一致性，数值实验数据的误差在可接受的范围以内，表明数值模型能够较好地反映船体所受的冰力均值特性，可应用于回转操纵的仿真计算。
3.2　回转操纵仿真结果
在计算船舶回转运动之前，首先进行螺旋桨转速与航速的匹配。设定螺旋桨以120 r/min的定转速对船体进行推进，并通过推进直航模拟确定稳定航速。通过模拟确定最终航速稳定在6.9 m/s（13.4 kn），对应的傅汝德数为0.215。
分别对船体模型在不同舵角δ、不同浮冰密集度C下的回转运动进行模拟。舵角δ分别设置为小舵角10°、中等舵角22.5°和大舵角30°，向船首右侧方向进行回转；浮冰密集度C分别设置为低密集度0.2、中密集度0.5、中高密集度0.6以及高密集度0.8，并与敞水工况的回转运动参数进行对比。
对30°舵角下的敞水以及浮冰密集度0.8两种典型工况进行比较，图8为两种航行工况的模拟回转轨迹。图9为浮冰密集度0.8航行工况不同时间对应的船舶回转照片，浮冰颗粒的颜色显示了浮冰颗粒的运动速度。回转开始阶段，船舶以较快的航速进入浮冰区，浮冰被船体冲散到船舷两侧。在这个阶段，浮冰与船体的接触主要发生在船首两侧。随着回转运动的进行，右舷的浮冰被船首推离，在较远处形成团状聚集区；左舷的浮冰则贴合船舷聚集，并在左舷方向形成宽度逐渐增加的带状聚集区，船舶的后方形成一道逐渐变宽的无冰水域；同时浮冰与船体的接触部位变化为船首右侧以及整个船体的左侧。
图10为两种航行工况下船舶所受到的纵向力X、侧向力Y和偏航力矩N的时历曲线。船舶在浮冰区进行回转运动时所受力与力矩数值波动剧烈，具有较强的随机性，其原因在于浮冰在船首处发生随机碰撞，并在船体周围发生翻转、堆积、挤压。同时，由于船舶所受冰阻力总体上随航速与浮冰尺寸的增加而增加[12，15，27]，船舶在回转初期所受力与力矩的峰值远大于稳定回转阶段。回转开始阶段，船舶以较大航速进入浮冰区，冰纵向力大小由航速与浮冰尺寸共同主导；随着回转运动的进行，船舶航速逐渐下降，冰纵向力大小转变为由浮冰尺寸主导。敞水工况下，当船舶进入稳定回转阶段，船舶所受纵向力X、侧向力Y逐渐趋向于某一数值附近，偏航力矩N则在0附近震荡。浮冰区工况下，纵向力X曲线出现的峰值体现了浮冰阻碍船舶前进的显著作用，侧向力Y与偏航力矩N曲线总体趋势与敞水工况相仿。
图11为上述两种工况的船舶航速时历曲线。浮冰区工况下，由于浮冰对船体碰撞产生纵向力作用，航速时历曲线在某些时间点出现突降，下降的幅度体现船体受到纵向力的幅值；同时，航速下降至一个相对稳定的速度后，仍会在一定的速度区间内产生波动与变化。回转过程中船体持续受到浮冰的复杂作用，导致船舶阻力与螺旋桨推力不能处于稳定的平衡状态，因此船舶航速起伏相对较大。此外，浮冰可能对螺旋桨性能产生影响而导致航速出现不稳定的变化，考虑实际航行情况，部分下沉的浮冰可能会对螺旋桨造成破坏作用，因此应当采取措施保护螺旋桨，并保证螺旋桨具有足够的强度。
图12为上述两种工况的船舶艏摇角速度时历曲线。敞水工况下，曲线从0开始增大到极大值，然后下降至一个稳定值，其趋势与图10（e）中偏航力矩N的时历曲线相关。40 s前偏航力矩为正值，对应艏摇角速度的上升区间；40 s到100 s间偏航力矩为负值，对应艏摇角速度的下降区间；100 s后偏航力矩在0附近震荡，对应艏摇角速度达到稳定，即船舶进入稳定回转阶段。浮冰区工况下，艏摇角速度时历曲线也经历了上升与下降的阶段，但由于浮冰的作用，曲线并不光滑，在某些时刻会产生突变，难以获得一个稳定值；同时艏摇角速度的最大值与100 s后的艏摇角速度值均小于敞水工况。
图13（a）、（b）、（c）分别为10°舵角、22.5°舵角、30°舵角下，不同浮冰密集度工况对应的回转轨迹。图14为各舵角工况对应的无量纲纵距AD/L随浮冰密集度的变化曲线，由图可见，10°舵角下，无量纲纵距AD/L随着浮冰密集度的增加产生较难预测的变化趋势；22.5°舵角下，各工况的AD/L变化不明显；30°舵角下，AD/L总体上随着浮冰密集度的增加而增加，在0.6密集度工况达到极值。与敞水工况相比，10°、22.5°、30°舵角条件下AD/L的最大增幅百分比分别为9.9%、2.5%和7.8%。
图15、图16分别为各舵角工况对应的无量纲横距TR/L和无量纲战术直径DT/L随浮冰密集度的变化曲线，由图可见，在各舵角下，TR/L和DT/L总体上均随着浮冰密集度的增加而增加，但其变化趋势并非线性。与敞水工况相比，10°、22.5°、30°舵角条件下TR/L的最大增幅百分比分别为19.1%、17.4%和29.2%；DT/L则分别为18.3%、17.9%和33.9%。
基于以上数据，在本文设定的航行条件下，出于安全考虑，船舶冰区航行遇障进行避碰操纵时，至少应比同舵角敞水工况提前15%的纵距距离进行转舵操作或提前降低航速。
图17分别为不同工况下x方向平均冰纵向力、流体纵向力以及总纵向力的变化趋势。在本文设定的坐标系下，船舶受到纵向力的方向均与随船坐标系x轴指向相反。为便于对比，图17中的数值均取其绝对值。航行过程中，回转运动造成航速下降，整体上冰纵向力占比较小，流体纵向力主导了总纵向力；尽管如此，在浮冰区工况下，船舶总纵向力均比敞水工况有显著增加。在各舵角下，总纵向力、冰纵向力均随浮冰密集度增加而增加，这是由于浮冰密集度越高，船与冰碰撞频次越高。相同舵角下，随着浮冰密集度的增加，流体纵向力变化不明显。
图18~19分别为不同工况下平均侧向力和平均偏航力矩的变化趋势。侧向力促成船舶在y方向上的偏移，偏航力矩则促成船舶绕z轴的转艏。在各舵角、不同浮冰密集度条件下，船舶的总侧向力与总偏航力矩均为正值，即总体上船舶受到的侧向力及偏航力矩方向与回转操纵方向一致；但是各工况下冰侧向力以及冰偏航力矩表现为正负不一。同时，在浮冰区工况下，船舶受到的总侧向力、流体侧向力均小于敞水工况，即浮冰的存在削弱了流体对船体在侧向上的作用，进而导致船舶回转直径的增加。
图20展示了船舶不同区域受到的冰侧向力Y1、Y2与Y3。船舶所受冰侧向力主要为作用在船首两侧的Y1与Y2，由航行过程中撞击静止的浮冰产生；船尾左侧的浮冰随船体滑动具有一定速度，故船尾左侧受到的冰侧向力Y3相对较小；船尾右侧不存在浮冰阻挡，基本不受冰侧向力作用。航行过程中船舶两侧受到浮冰碰撞具有随机性，碰撞浮冰的尺寸大小不一，故导致平均冰侧向力的方向难以预测。同时冰侧向力Y1与Y3共同构成与船舶转艏方向相反的力矩，Y2则产生与船舶转艏方向相同的力矩，二者作用相反，故导致平均冰偏航力矩正负不一。尽管如此，从图19可知，绝大多数工况的平均冰偏航力矩为负值（力矩方向与船舶转艏方向相反），即总体上浮冰的存在对船舶的转艏产生了阻碍作用。
对比图10的时历曲线与图17-19，时历曲线中出现的峰值与均值对比具有不同的数量级，对船体结构产生较大冲击的纵向力最大峰值数量级可达107 N。观察回转轨迹可知，船舶并没有因为受到浮冰的碰撞而在极短的时间内发生轨迹的突变，表明在本文设定的航行条件下，流体对船体的作用仍是促成船舶回转运动的主要因素；浮冰对船舶回转运动的影响通过一定时间的累积才会显现。
4　结论
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本文采用CFD-DEM相结合的方法，针对一艘中型极地船舶在浮冰区中的回转操纵过程进行了数值仿真研究，考虑了舵角、浮冰密集度等参数，对船舶回转运动的参数进行预报，得到如下结论：
（1）船舶在回转的不同阶段与浮冰有不同的接触模式与接触位置，船体受到的力与力矩随机性强。浮冰区船舶回转运动的航速时历曲线总体上起伏较大，并在某些时间点会出现突然下降的变化。浮冰区工况下艏摇角速度的最大值，以及船舶进入稳定回转阶段时间点（注：本文算例中对应t=100 s）后的艏摇角速度值均小于敞水工况。
（2）浮冰的存在会对船舶的回转运动产生显著阻碍。在本文设定的航行条件下，出于安全考虑，船舶冰区航行遇障进行避碰操纵时，至少应比同舵角敞水工况提前15%的纵距距离进行转舵操作或提前降低航速；浮冰区工况战术直径的范围为敞水工况战术直径的1倍到1.5倍。
（3）浮冰区工况下，流体纵向力主导了x方向总纵向力，但总纵向力仍比敞水工况有显著增加；冰纵向力随着浮冰密集度的增加而增加，流体纵向力变化不明显。船舶受到的平均总侧向力及总偏航力矩方向与回转操纵方向一致，平均冰侧向力的方向随机性较强，平均冰偏航力矩方向更多偏向于与回转操纵方向相反。同时，回转过程中船舶所受冰力的峰值与均值对比具有不同的数量级，在进行船体结构设计时需要着重考虑。
基金
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  • 工信部高技术船舶科研项目(MC-201918-C10)
文献
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2025年第29卷第7期
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doi: 10.3969/j.issn.1007-7294.2025.07.003
  • 接收时间：2025-01-22
  • 首发时间：2026-03-24
  • 出版时间：2025-07-20
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  • 收稿日期：2025-01-22
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工信部高技术船舶科研项目(MC-201918-C10)
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    1.天津大学　建筑工程学院，天津　300072
    2.国家管网西南管道公司输油气分公司，南宁　530200
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2种不同金属材料的力学参数
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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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