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Article(id=1243896351193412554, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243896350367134664, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2025.09.003, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1742140800000, receivedDateStr=2025-03-17, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774497600600, onlineDateStr=2026-03-26, pubDate=1758297600000, pubDateStr=2025-09-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774497600600, onlineIssueDateStr=2026-03-26, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774497600600, creator=13701087609, updateTime=1774497600600, updator=13701087609, issue=Issue{id=1243896350367134664, tenantId=1146029695717560320, journalId=1240685776644648972, year='2025', volume='29', issue='9', pageStart='1343', pageEnd='1498', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774497600404, creator=13701087609, updateTime=1774501609474, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1243913165692584796, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243896350367134664, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1243913165692584797, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243896350367134664, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1361, endPage=1372, ext={EN=ArticleExt(id=1243896351575094219, articleId=1243896351193412554, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Numerical simulation on the hydrodynamics of a near-surface self-propelled submarine, columnId=1241023037940748650, journalTitle=Journal of Ship Mechanics, columnName=Hydrodynamics, runingTitle=null, highlight=null, articleAbstract=

In order to meet the needs of the evaluation and optimization of submarine near-surface navigation performance, this paper performs a numerical study on the hydrodynamic characteristics of a near-surface self-propelled submarine by using Reynolds-Averaged Navier-Stokes method. The volume of fluid model is used to capture the interaction between submarine and free surface, and the body force model is used to establish the propeller hydrodynamic model. At the same time, the controllers of propeller and stern rudders are constructed to control the speed and course of the submarine, and the numerical simulation of the submarine near-surface self-propulsion test is realized. The numerical simulation results are compared with the model test data and numerical simulation results from other literature, and the effectiveness of the established numerical method is thus verified. Through the numerical simulation of the submarine self-propulsion test under different immersion depth, the variation law of the submarine near-surface self-propulsion point with the immersion depth is revealed, and the internal mechanism is discussed by combining the flow field characteristics obtained from numerical simulation.

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针对潜艇近水面航行性能评估及优化需要，本文基于雷诺平均方法对潜艇近水面自航水动力特性开展数值模拟研究。采用流体体积法两相流模型捕捉潜艇与自由液面之间的相互作用，采用体积力建模方法建立螺旋桨水动力模型；同时，构造螺旋桨及艉舵控制器实时控制潜艇航速及航向，实现潜艇近水面自航试验数值模拟。将数值模拟结果与相关文献中公开的模型试验数据及数值模拟结果进行对比，验证了所建立数值方法的有效性。通过不同浸深下的潜艇自航试验数值模拟，揭示了潜艇近水面自航点随浸深的变化规律，并结合数值模拟获得的流场信息对其内在机理进行分析探讨。

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通讯作者，E-mail：
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郭海鹏（1988-），男，博士，副教授，E-mail：

李广年（1980-），男，博士，教授，通讯作者，E-mail：。

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郭海鹏（1988-），男，博士，副教授，E-mail：

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郭海鹏（1988-），男，博士，副教授，E-mail：

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李广年（1980-），男，博士，教授，通讯作者，E-mail：。

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李广年（1980-），男，博士，教授，通讯作者，E-mail：。

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Principal dimensions of the Joubert BB2 submarine

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参数符号/单位实尺度模型尺度
艇长Loa/m70.23.826
艇宽B/m9.60.5232
甲板高度Dd/m10.60.5777
围壳高度Ds/m16.20.8829
螺旋桨直径Dp/m50.273
排水量∇/t44400.7012
重心纵向位置XCG/m32.311.761
重心垂向位置ZCG/m0.04430.0024
浮心垂向位置XCB/m5.6440.024 21
横摇惯性半径rx/m3.4330.1871
纵摇惯性半径ry/m17.60.9592
首摇惯性半径rz/m17.5220.9550
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Joubert BB2潜艇主尺度

, figureFileSmall=null, figureFileBig=null, tableContent=
参数符号/单位实尺度模型尺度
艇长Loa/m70.23.826
艇宽B/m9.60.5232
甲板高度Dd/m10.60.5777
围壳高度Ds/m16.20.8829
螺旋桨直径Dp/m50.273
排水量∇/t44400.7012
重心纵向位置XCG/m32.311.761
重心垂向位置ZCG/m0.04430.0024
浮心垂向位置XCB/m5.6440.024 21
横摇惯性半径rx/m3.4330.1871
纵摇惯性半径ry/m17.60.9592
首摇惯性半径rz/m17.5220.9550
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Immersion depth conditions

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工况D0/LoaDsw/Loa工况D0/LoaDsw/Loa
1∞∞70.2190.057
20.5000.33780.1980.036
30.3050.14290.1720.010
40.2830.121100.150−0.013
50.2620.100110.107−0.056
60.2410.078120.064−0.098
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浸深工况

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工况D0/LoaDsw/Loa工况D0/LoaDsw/Loa
1∞∞70.2190.057
20.5000.33780.1980.036
30.3050.14290.1720.010
40.2830.121100.150−0.013
50.2620.100110.107−0.056
60.2410.078120.064−0.098
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Automatic control parameters (model scale)

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参数PuPyDuDyPΨDΨ
数值18.3—18.3—3.02.8
), ArticleFig(id=1243896374996087435, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896351193412554, language=CN, label=表3, caption=

自动控制器参数（模型尺度）

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参数PuPyDuDyPΨDΨ
数值18.3—18.3—3.02.8
), ArticleFig(id=1243896375096750734, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896351193412554, language=EN, label=Tab.4, caption=

Influence of grid scale and time step on the numerical results

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原始设置网格尺度加密相对偏差时间步长加密相对偏差
转速n/（r·min−1）268.458268.3220.051%268.4540.001%
推力T/N23.32423.500−0.753%23.327−0.012%
), ArticleFig(id=1243896375218385552, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896351193412554, language=CN, label=表4, caption=

网格尺度及时间步长对数值结果的影响

, figureFileSmall=null, figureFileBig=null, tableContent=
原始设置网格尺度加密相对偏差时间步长加密相对偏差
转速n/（r·min−1）268.458268.3220.051%268.4540.001%
推力T/N23.32423.500−0.753%23.327−0.012%
), ArticleFig(id=1243896375340020371, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896351193412554, language=EN, label=Tab.5, caption=

Comparison of numerical results with data from other literatures

, figureFileSmall=null, figureFileBig=null, tableContent=
EFDReFRESCO PROCALReFRESCO DiscretizedREX本文计算与测试结果对比误差
转速n/（r·min−1）63.161.063.564.262.70.63%
推力T/kN161.5154.4157.2156.3148.08.34%
), ArticleFig(id=1243896375461655190, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896351193412554, language=CN, label=表5, caption=

本文数值结果与文献[8]中的数据对比

, figureFileSmall=null, figureFileBig=null, tableContent=
EFDReFRESCO PROCALReFRESCO DiscretizedREX本文计算与测试结果对比误差
转速n/（r·min−1）63.161.063.564.262.70.63%
推力T/kN161.5154.4157.2156.3148.08.34%
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潜艇近水面自航水动力数值模拟
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郭海鹏 1 , 李广年 1 , 周剑 2 , 葛俊宇 1 , 杜林 1
船舶力学 | 流体力学 2025,29(9): 1361-1372
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船舶力学 | 流体力学 2025, 29(9): 1361-1372
潜艇近水面自航水动力数值模拟
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郭海鹏1 , 李广年1 , 周剑2, 葛俊宇1, 杜林1
作者信息
  • 1.宁波大学　海运学院，浙江　宁波　315211
  • 2.中国船舶科学研究中心，江苏　无锡　214082

    • 郭海鹏（1988-），男，博士，副教授，E-mail：

    李广年（1980-），男，博士，教授，通讯作者，E-mail：。

通讯作者:

通讯作者，E-mail：
Numerical simulation on the hydrodynamics of a near-surface self-propelled submarine
Hai-peng GUO1 , Guang-nian LI1 , Jian ZHOU2, Jun-yu GE1, Lin DU1
Affiliations
  • 1.Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China
  • 2.China Ship Scientific Research Center, Wuxi 214082, China
出版时间: 2025-09-20 doi: 10.3969/j.issn.1007-7294.2025.09.003
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摘要
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针对潜艇近水面航行性能评估及优化需要，本文基于雷诺平均方法对潜艇近水面自航水动力特性开展数值模拟研究。采用流体体积法两相流模型捕捉潜艇与自由液面之间的相互作用，采用体积力建模方法建立螺旋桨水动力模型；同时，构造螺旋桨及艉舵控制器实时控制潜艇航速及航向，实现潜艇近水面自航试验数值模拟。将数值模拟结果与相关文献中公开的模型试验数据及数值模拟结果进行对比，验证了所建立数值方法的有效性。通过不同浸深下的潜艇自航试验数值模拟，揭示了潜艇近水面自航点随浸深的变化规律，并结合数值模拟获得的流场信息对其内在机理进行分析探讨。

潜艇  /  近水面  /  自航试验  /  计算流体动力学

In order to meet the needs of the evaluation and optimization of submarine near-surface navigation performance, this paper performs a numerical study on the hydrodynamic characteristics of a near-surface self-propelled submarine by using Reynolds-Averaged Navier-Stokes method. The volume of fluid model is used to capture the interaction between submarine and free surface, and the body force model is used to establish the propeller hydrodynamic model. At the same time, the controllers of propeller and stern rudders are constructed to control the speed and course of the submarine, and the numerical simulation of the submarine near-surface self-propulsion test is realized. The numerical simulation results are compared with the model test data and numerical simulation results from other literature, and the effectiveness of the established numerical method is thus verified. Through the numerical simulation of the submarine self-propulsion test under different immersion depth, the variation law of the submarine near-surface self-propulsion point with the immersion depth is revealed, and the internal mechanism is discussed by combining the flow field characteristics obtained from numerical simulation.

submarine  /  near-surface  /  self-propulsion test  /  computational fluid dynamics
郭海鹏, 李广年, 周剑, 葛俊宇, 杜林. 潜艇近水面自航水动力数值模拟. 船舶力学, 2025 , 29 (9) : 1361 -1372 . DOI: 10.3969/j.issn.1007-7294.2025.09.003
Hai-peng GUO, Guang-nian LI, Jian ZHOU, Jun-yu GE, Lin DU. Numerical simulation on the hydrodynamics of a near-surface self-propelled submarine[J]. Journal of Ship Mechanics, 2025 , 29 (9) : 1361 -1372 . DOI: 10.3969/j.issn.1007-7294.2025.09.003
正文
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0　引言
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快速性是潜艇设计过程中需要考虑的最重要的水动力性能之一，也是反映其生存能力和执行任务能力的重要标志。作为预报潜艇快速性能的主要手段，自航试验一直以来都是潜艇设计过程中的重要环节，且对于探讨艇体与螺旋桨之间的相互干扰问题十分关键。然而，不同于水面舰船，潜艇具有多航态的特性，既包括深潜（无限水深）航行状态，还包括近海底、近水面以及水面航行状态。在物理水池中开展的潜艇自航试验研究存在诸多局限性，如测量仪器产生的干扰以及试验过程中存在的兴波干扰等问题[1]。
近年来，计算流体动力学（Computational Fluid Dynamics，CFD）方法在船舶及水下航行器水动力问题研究方面得到了大量应用，也成为开展潜艇自航试验研究的有力工具。张楠等[2]明确了潜艇阻力、螺旋桨敞水特性以及艇/桨水动力干扰的计算方法，并对潜艇快速性数值预报精度进行了分析。杨琴等[3]系统研究了带桨全附体潜艇的三维粘性流场和水动力特性，探讨了带桨潜艇表面的压力分布及桨后尾流速度场的绕轴线螺旋状分布规律。吕晓军等[4]采用体积力模拟螺旋桨力场，对潜艇自航因子进行了预报，并与带桨潜艇自航试验数值模拟的结果进行了对比。Chase等[5]对全附体潜艇的自航试验进行了数值模拟，着重探讨了潜艇自航状态下的螺旋桨尾流场特性。
潜艇在近水面和水面航行时会引起自由面兴波，导致其绕流场特性极为复杂。张楠等[6-7]对某潜艇模型近海底和近水面绕流进行了数值模拟，分析了不同浸深下的潜艇阻力、自由面波形特性以及艇/桨干扰特性。Carrica等[8]对不同浸深下潜艇自航试验进行了数值模拟，探讨了浮态控制对潜艇自航状态的影响。Wang等[9]对全附体潜艇模型在近水面处的绕流场进行了数值模拟，分析了船体伴流及自由液面对螺旋桨尾流场特性的影响。李鹏等[10]对潜艇近水面航行绕流场进行数值模拟，分析了近水面航行潜艇自航状态下的流动特征及螺旋桨水动力载荷特征。朱信尧等[11]研究了浸深对近水面潜体与自由液面耦合作用的影响，得到了浸深对潜体水动力参数及自由液面兴波的影响规律。
从目前已有研究来看，针对潜艇近水面自航水动力特性的数值研究相对有限，特别是对于自航点随浸深变化等相关研究较少见诸于文献。本文基于商用粘性流体力学计算平台STAR-CCM+，对潜艇近水面自航水动力展开数值模拟研究。采用雷诺平均（Reynolds-Averaged Navier-Stokes，RANS）方法以及流体体积法（Volume of Fluid，VOF）两相流模型求解潜艇近水面航行绕流场，其中螺旋桨采用体积力模型进行水动力建模。同时，构造比例-微分控制器（Proportion Derivative，PD）对潜艇航速和航向进行控制，从而实现潜艇近水面自航试验的数值模拟。此外，通过不同浸深下的潜艇自航试验数值模拟，探讨浸深对潜艇近水面自航状态下的水动力及流场特性的影响。
1　数值方法
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1.1　基本理论
潜艇航行过程中的绕流场具有粘性、不可压特性，可用RANS方法进行求解，控制方程如下：
式中，ρ为流体密度，和分别为平均速度和平均压力，t为时间，I为单位应力张量，T为粘性应力张量，fb为作用在流体上的体积力（如重力、离心力等），Tt为雷诺应力张量。
由于雷诺应力项Tt的存在，需要引入湍流模型对控制方程进行封闭。目前应用较广泛的湍流模型是标准k-ε模型，该模型通过湍流动能输运方程和湍流耗散率输运方程来描述湍流，但方程的推导依赖于现象和经验，在复杂流动预测方面存在局限性。本文采用的Realizable k-ε湍流模型是标准k-ε模型的改进形式，该模型引入了更为合理的湍流粘度公式，并基于准确的涡度脉动输运方程推导了修正的湍流耗散率输运方程，在边界层流动、分离流动等复杂流动预测方面的有效性已得到验证。
数值迭代过程中，空间离散采用二阶迎风格式，时间离散采用一阶迎风格式，利用SIMPLE（Semi-Implicit Method for Pressure-lined Equation）算法对速度和压力耦合进行求解。针对潜艇近水面航行时产生的自由液面兴波，采用VOF两相流模型来捕捉不同流体相间自由界面的变化。
1.2　螺旋桨建模
从计算精度和计算效率相平衡的角度出发，采用Hough等[12]提出的体积力模型对艇后螺旋桨进行水动力建模。该方法将螺旋桨替换为虚拟激励盘，激励盘模型基于螺旋桨敞水特性曲线构造。螺旋桨对周围流场的扰动通过在盘体区域的控制方程中施加体积力源项的方式加以考虑，体积力fb沿周向均匀分布在虚拟盘体上，其径向分布遵循Goldstein最佳分布，由以下公式定义：
式中，fbx为轴向体积分力，fbθ为切向体积分力，r为径向半径，RH为桨毂半径，RP为螺旋桨叶尖半径。此外，式（3）~（4）中的常数由下式进行计算：
式中，T为推力，Q为扭矩，∆为虚拟盘体厚度。
1.3　自动控制器
潜艇近水面航行时的绕流特性与深潜航行相比有所不同，其自航点会随浸深发生变化。而且，由于螺旋桨尾流的周向诱导效应，使得零舵角下仍存在一定的舵力，故需要通过压舵角来保证航向。因此，需要构造PD控制器以便在数值模拟过程中实时调整螺旋桨转速及方向舵舵角，以保证潜艇自航过程中的航速及航向，其基本工作原理如图1所示。
螺旋桨转速n和方向舵舵角δ的PD控制器的数学表达如下：
式中，u为纵向速度，为纵向加速度，y为横向位移，为横向速度，Ψ为首向角，为转首角速度，∆表示设定值与当前值之间的差值，变量前的系数为控制参数。
2　研究对象
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2.1　几何模型
研究对象为通用型潜艇模型Joubert BB2，该模型的初始设计概念由Joubert[13-14]在2004年提出。MARIN水池的Overpelt等[15]在原始方案基础上进行了改进，改进后的模型被广泛用于潜艇水动力性能验证研究。该潜艇主艇体为圆柱状平行中体，附体包括坐落在平行中体前部的流线型围壳、围壳舵以及艇艉的X型艉舵，此外艉部配有6叶的MARIN 7371R螺旋桨，整个潜艇的几何外形如图2所示。潜艇的X型艉舵由4片舵叶组成，舵轴中心线与艇的中纵剖面夹角为45°，舵叶可绕各自轴线旋转，从而使艇体发生水平和垂向运动，如图3所示。参考MARIN水池的模型试验，在模型尺度下进行数值研究，模型缩尺比为18.348，主尺度如表1所示。
MARIN水池以Joubert BB2潜艇模型为研究对象开展了一系列模型试验[15]，包括直航、回转以及Z形运动等，试验过程中潜艇通过艉舵控制器实现潜艇航向和潜深控制。对于X型艉舵，在舵角控制器中要采用等效舵角，表达式如下：
式中，δH为等效方向舵角，δV为等效升降舵角，各分舵角以指向艇体外侧为正。
2.2　研究工况
本文开展不同浸深下的潜艇近水面自航试验数值模拟，具体工况如表2所示。为了全面反映其浸深情况，分别采用艇体轴线至水面距离D0、围壳顶部至水面距离Dsw对浸深工况进行描述。潜艇模型尺度航速为1.2 m/s，实尺度航速为10 kn，对应傅汝德数为0.196。此外，考虑到潜艇在近水面处仅靠艉舵难以保持垂向位置，在数值模拟过程中未放开垂荡及纵摇自由度，仅对螺旋桨转速和方向舵舵角进行控制，控制器参数取值如表3所示。
3　数值计算参数设置
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图4给出了数值模拟所采用的计算域，计算域尺度如下：以潜艇艉部端点为参考位置，入流面距离为5.23Loa，出流面距离为7.84Loa，左右边界距离为5.23Loa，上下边界距离为2.62Loa。计算域整体采用切割体网格进行离散。为了准确模拟潜艇附近区域的流场特性，对围壳及艉部附近进行了网格加密处理。在靠近壁面区域采用了6层棱柱形网格，使壁面无因次距离Y+值控制在30左右。此外，考虑到自由面兴波的捕捉精度，在水线面附近对网格进行了垂向加密处理。螺旋桨体积力模型入流面设为桨盘前0.1Dp处，虚拟激励盘及螺旋桨尾流区域也进行了网格加密。由于在模拟过程中需要控制艉舵舵角以保证航向，将计算域分为舵旋转区域和整体区域，两者之间采用重叠网格以保证两个区域间的信息传递。图5给出了螺旋桨、艉舵的处理及网格划分情况。
深潜工况（无自由面加密）计算域网格数量约为400万，近水面工况计算域网格数量约为460万，时间步长设为0.04 s，物理模拟时间为100 s。此外，考虑到网格尺度及时间步长的选取是否合理也会影响计算结果的可靠性，选取深潜工况的潜艇自航试验为研究案例，分别进行网格尺度和时间步长收敛性分析。网格尺度收敛性分析采用中、细两套网格，网格数量分别为400万、950万。图6和图7分别给出了两套网格的整体及局部的网格分布对比。时间步长收敛性分析也采用中、细两种时间步长，时间步长分别为0.04 s、0.02 s。
4　数值计算结果
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4.1　自航点
图8给出了深潜工况下数值模拟获得的螺旋桨转速及推力时历变化曲线。如图所示，在螺旋桨转速和方向舵舵角控制器作用下，潜艇在100 s内达到运动稳定状态。网格尺度及时间步长对迭代过程及收敛结果均有一定影响，其中网格尺度的影响更为明显。为了进一步分析网格尺度及时间步长对数值结果的影响，表4给出收敛状态下的自航点计算结果对比。如表所示，网格尺度及时间步长对自航点螺旋桨推力及转速计算结果影响相对较小，引起的相对偏差绝对值小于1%，表明当前研究所采用的网格尺度及时间步长具有较好的数值稳定性。
表5给出了本文数值计算结果与文献[8]中公开的模型试验及数值计算结果的对比。为了便于对比分析，本文计算结果也采用与上述文献中相同的处理方法，将模型尺度结果换算为实尺度结果。从表中可以看出，本文数值计算得到的自航点螺旋桨转速及推力相对于模型试验结果偏低，其中自航点螺旋桨转速误差为0.63%，推力误差为8.34%。实际上，模型试验过程中潜艇存在一定的纵倾，而本文数值模拟过程中潜艇始终处于正浮状态，这也导致数值模拟获得的自航点螺旋桨转速及推力相对试验值偏低。此外，体积力模型对艇/桨干扰流场的简化处理也是引起偏差的原因之一。表中也给出了其他求解器获得的数值结果，其中ReFRESCO PROCAL采用了基于边界元法的螺旋桨体积力模型，而ReFRESCO Discretized和REX采用了螺旋桨真实几何模型。通过对比发现，本研究数值方法与文献中公开的数值计算结果基本相当，这也进一步验证了本研究数值计算方法的有效性。
图9给出了不同浸深条件下的近水面工况自航点计算结果。从图中可以看出，浸深D0/Loa>0.3时，潜艇自航点螺旋桨转速及推力基本不随浸深变化，这与以往研究得到的结果[7]相一致。浸深D0/Loa<0.3时，潜艇自航状态下的螺旋桨转速及推力明显增加。浸深D0/Loa=0.15附近，自航状态下的螺旋桨转速及推力达到峰值。值得注意的是，浸深D0/Loa进一步减小时，自航状态下的螺旋桨转速及推力出现了显著下降。然而，随着浸深D0/Loa的进一步减小，自航状态下的螺旋桨转速及推力又显著增大。此外，图中还给出了Carrica等[16]的计算结果，其采用了更精确的螺旋桨水动力建模方法。通过对比发现，本文计算结果在趋势上与文献中的计算结果一致，这也在一定程度上验证了本文数值计算结果的可靠性。
4.2　兴波特性
图10~14分别给出了浸深D0/Loa=0.198、0.172、0.150、0.107、0.064时的潜艇自由面兴波及中纵剖面处波形轮廓。浸深D0/Loa=0.198时，尽管潜艇围壳顶端低于水面且有一定距离，但已经出现了较为明显的自由面兴波现象，围壳上方的自由液面出现了明显的伯努利水丘，其中以围壳上方的波谷及后方的波峰尤为显著。浸深D0/Loa=0.172时，潜艇围壳顶部低于水面但距离较小，伯努利水丘形状发生显著变化，围壳前端处自由液面形成了明显的波峰，后端处的波谷和波峰显著加强，波谷处自由液面高度低于围壳顶端，而后方的波峰形状也发生变化，并出现了一定的兴波破碎现象，总体而言，该浸深条件下的潜艇自由面兴波更为显著。浸深D0/Loa=0.150时，潜艇围壳顶部高于水面，围壳前端的波峰、后端的波谷及波峰更为显著。在以上浸深范围内，潜艇航行所产生的自由面兴波随浸深的减小逐渐加强，从能量角度而言，艇体受到的兴波阻力也越来越大，这也是导致自航点螺旋桨转速及推力随浸深不断增加的重要因素。
浸深D0/Loa=0.107时，潜艇围壳大部分高于水面，其引起的自由面兴波特性也发生明显变化。此时，由于围壳兴波的波峰与艇艏兴波的波谷相互叠加，导致围壳附近的兴波有所减弱。同时，由于艇体靠近水面，使得艇体后部自由液面也出现了伯努利水丘。但总体而言，该浸深下的潜艇兴波整体有所减弱。浸深D0/Loa=0.064时，潜艇艇体甲板也位于水面以上，与水面舰船类似，在艇体附近形成了显著的自由面兴波，尤其是艇艏附近出现了大幅的波峰和波谷，这也导致潜艇的兴波阻力显著上升。
4.3　艇艉流场
图15~19分别给出了浸深D0/Loa=0.198、0.172、0.150、0.107、0.064时的艇艉区域及螺旋桨入流面的轴向速度分布。其中，艇艉区域轴向速度分布云图中的红色虚线框代表螺旋桨激励盘，螺旋桨入流面轴向速度分布云图中的红色虚线圆圈代表螺旋桨盘面。浸深D0/Loa=0.198、0.172、0.150时，艇艉区域距离自由液面有一定距离，螺旋桨附近流场基本不受影响。因此，在上述工况中自航点螺旋桨转速及推力随浸深增加主要是由于艇体自由面兴波引起的兴波阻力所致。
浸深D0/Loa=0.107时，艇艉区域流场受到艇体兴波影响较为明显，桨盘面前方的入流速度显著下降，这意味着螺旋桨转速一定时其进速减小而推力增大。同时，由于该浸深下的艇体自由面兴波有所减弱，艇体受到的兴波阻力也有所下降。由于上述两方面因素的影响，导致该浸深下出现了自航点螺旋桨转速及推力骤降的现象。浸深D0/Loa=0.064时，艇艉区域的流场受到艇体兴波的影响加剧。值得注意的是，该工况下的桨盘面前方入流速度反而有所增大，这意味着螺旋桨转速一定时进速增大而推力减小。同时，由于该浸深工况下潜艇自由面兴波十分显著，因此也导致自航点螺旋桨转速和推力显著增大。
5　结论
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本文应用RANS方法、VOF两相流模型以及螺旋桨体积力模型建立了潜艇近水面自航试验的数值模拟方法，并结合螺旋桨转速及方向舵舵角控制器实现了不同浸深下的潜艇自航状态的数值模拟，在此基础上对潜艇近水面自航水动力特性进行了研究，得到的主要结论如下：
（1）基于体积力模型的螺旋桨水动力建模方法在深潜及近水面工况下的潜艇自航试验数值模拟方面具有较好的适用性，通过与相关文献中公开的模型试验数据及数值模拟结果对比，本文所建立的潜艇近水面自航试验数值模拟方法在自航点的螺旋桨转速及推力预报方面达到了令人满意的精度，获得了与公开文献中相一致的自航点随浸深变化规律，表明螺旋桨体积力模型也能较好地处理潜艇近水面自航过程中的艇/桨相互作用问题，为开展相关问题研究提供了实用高效的手段和工具。
（2）潜艇近水面工况下的自航水动力随浸深呈现较为复杂的变化规律，通过分析流场信息发现，这与其兴波特性及艇艉流场有密切联系。浸深D0/Loa>0.3时，自由液面对潜艇自航水动力的影响基本可以忽略。浸深D0/Loa=0.15~0.3时，艇体自由面兴波较为明显而艇艉区域流场则基本不受影响，此时前者是自航点螺旋桨转速及推力增加的主要原因。浸深D0/Loa=0.1附近时，艇体自由面兴波整体减弱，而桨盘面前入流速度整体下降，这是导致该工况下自航点螺旋桨转速及推力骤降的原因。随着浸深进一步减小，艇体兴波尤其是艇艏兴波显著加强，桨盘面前入流速度有所上升，引起自航点螺旋桨转速及推力再次增加。
尽管体积力模型在潜艇近水面自航试验数值模拟过程中表现出比较好的效果，但对于深入研究自由液面与螺旋桨之间的相互作用、倒车制动等复杂操纵工况下的运动特性等存在明显的局限性，下一步拟针对该方面开展相关研究。
基金
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  • 国家自然科学基金资助项目(52201367; 52171263)
  • 浙江省自然科学基金资助项目(LQ22E090003)
文献
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2025年第29卷第9期
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doi: 10.3969/j.issn.1007-7294.2025.09.003
  • 接收时间：2025-03-17
  • 首发时间：2026-03-26
  • 出版时间：2025-09-20
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  • 收稿日期：2025-03-17
基金
国家自然科学基金资助项目(52201367; 52171263)
浙江省自然科学基金资助项目(LQ22E090003)
作者信息
    1.宁波大学　海运学院，浙江　宁波　315211
    2.中国船舶科学研究中心，江苏　无锡　214082

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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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