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Article(id=1242150712109511315, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1242150711367119505, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2024.04.003, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1698076800000, receivedDateStr=2023-10-24, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774081407811, onlineDateStr=2026-03-21, pubDate=1713542400000, pubDateStr=2024-04-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774081407811, onlineIssueDateStr=2026-03-21, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774081407811, creator=13701087609, updateTime=1774081407811, 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=501, endPage=512, ext={EN=ArticleExt(id=1242150712319226516, articleId=1242150712109511315, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Maneuverability prediction of channel-type unmanned catamarans, columnId=1241023037940748650, journalTitle=Journal of Ship Mechanics, columnName=Hydrodynamics, runingTitle=null, highlight=null, articleAbstract=

Path planning is one of the key technologies for autonomous navigation of unmanned vehicles. A good path planning method is of great significance to the intelligent development of unmanned vehicles. In the existing path planning research, the maneuvering performance of unmanned vehicles is not considered. In order to make the planned path have shorter voyage time, shorter path length and better path tracking ability, it is necessary to combine the maneuvering performance of unmanned vehicles with the path planning algorithm. In order to accurately predict the ship maneuverability, the channel-type unmanned catamaran was taken as the research object, and simulation tests of three planar motion mechanisms were carried out by CFD technology. Simulation results were fitted with different hydrodynamic models, and corresponding hydrodynamic derivatives were calculated. The MMG model was used to establish a mathematical model of ship maneuvering motion to simulate the turning motion and Z-shape motion of the unmanned catamaran. The influence of different hydrodynamic models on the simulation results was analyzed, and the maneuvering pre-diction of the unmanned catamaran was realized.

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路径规划是无人艇实现自主航行的关键技术之一，良好的路径规划方法对无人艇的智能化发展具有重要意义。而在已有的路径规划研究中，并未考虑无人艇的操纵性能。为了使规划的路径具有较短的航行时间、路径长度以及较优的路径跟踪能力，需将无人艇自身的操纵性能与路径规划算法相融合。为精确地预测船舶的操纵性能，本文以槽道型无人双体船为研究对象，通过CFD技术开展斜航、纯横荡和纯艏摇三种平面运动机构仿真试验，使用不同水动力模型对仿真结果进行拟合，计算得到相应的水动力导数。同时采用MMG模型，建立船舶操纵运动数学模型，模拟无人双体船的回转运动和Z形运动，分析不同水动力模型对仿真结果的影响，并实现无人双体船的操纵性预报。

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通讯作者，E-mail：
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刘冬雨（1996-），女，博士研究生

高霄鹏（1971-），女，博士，副教授

霍聪（1989-），男，博士，副教授，通讯作者，E-mail：。

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刘冬雨（1996-），女，博士研究生

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刘冬雨（1996-），女，博士研究生

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高霄鹏（1971-），女，博士，副教授

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高霄鹏（1971-），女，博士，副教授

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霍聪（1989-），男，博士，副教授，通讯作者，E-mail：。

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霍聪（1989-），男，博士，副教授，通讯作者，E-mail：。

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Fluids Eng., 2001, 123(4): 793-802., articleTitle=Comprehensive approach to verification and validation of CFD simulations—Part 1: Methodology and procedures, refAbstract=null), Reference(id=1242150731193594081, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, doi=null, pmid=null, pmcid=null, year=2004, volume=126, issue=4, pageStart=704, pageEnd=706, url=null, language=null, rfNumber=[12], rfOrder=14, authorNames=Wilson R, Shao J, Stern F, journalName=J. Fluids Eng., refType=null, unstructuredReference=Wilson R, Shao J, Stern F. Discussion: Criticisms of the “correction factor” verification method[J]. J. 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figureFileSmall=K7MvornXTXPxQUOyor0B7A==, figureFileBig=1fxHJPW+vacTp07+vmzQlQ==, tableContent=null), ArticleFig(id=1242150725044745198, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=EN, label=Fig.6, caption=Fitting results of oblique shipping motion, figureFileSmall=k+p1g0CEFFrg9jQKrSLFhg==, figureFileBig=jH2lagqnirPacNlaCd+7Ow==, tableContent=null), ArticleFig(id=1242150725128631283, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=CN, label=图6, caption=斜航运动的拟合结果, figureFileSmall=k+p1g0CEFFrg9jQKrSLFhg==, figureFileBig=jH2lagqnirPacNlaCd+7Ow==, tableContent=null), ArticleFig(id=1242150725220905974, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=EN, label=Fig.7, caption=Wave-forming cloud around the ship with the amplitude of 0.1 m and 0.2 m, figureFileSmall=YVwnN9+ooUuOSc/ZowAzyg==, figureFileBig=Sa6KYGz6ib347cxy0NlOyA==, tableContent=null), ArticleFig(id=1242150725325763576, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=CN, label=图7, caption=振幅分别为0.1 m、0.2 m时的船体周围兴波云图, figureFileSmall=YVwnN9+ooUuOSc/ZowAzyg==, figureFileBig=Sa6KYGz6ib347cxy0NlOyA==, tableContent=null), ArticleFig(id=1242150725405455354, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=EN, label=Fig.8, caption=Fitting curve of pure swing motion, figureFileSmall=MS1hO4avuNp1SjUGGcUS2g==, figureFileBig=f/WJ2CMsfTh5T44EEhp+sA==, tableContent=null), ArticleFig(id=1242150725506118656, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=CN, label=图8, caption=纯横荡运动的拟合曲线, figureFileSmall=MS1hO4avuNp1SjUGGcUS2g==, figureFileBig=f/WJ2CMsfTh5T44EEhp+sA==, tableContent=null), ArticleFig(id=1242150725594198017, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=EN, label=Fig.9, caption=Wave-forming cloud around the ship when the amplitude is 0.1 m and 0.05 m respectively, figureFileSmall=JqfArxmqgUhlFDMX8nGJvg==, figureFileBig=PYHnQ+TL3uw4hZ8HKt/iBg==, tableContent=null), ArticleFig(id=1242150725665501188, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=CN, label=图9, caption=振幅分别为0.1 m、0.05 m时的船体周围兴波云图, figureFileSmall=JqfArxmqgUhlFDMX8nGJvg==, figureFileBig=PYHnQ+TL3uw4hZ8HKt/iBg==, tableContent=null), ArticleFig(id=1242150725774553097, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=EN, label=Fig.10, caption=Numerical simulation results of pure bow rolling motion, figureFileSmall=NNpdZiLTivftX/09jQ+sIw==, figureFileBig=BaI+O/iILwKNIYUWlNMLsQ==, tableContent=null), ArticleFig(id=1242150725879410702, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=CN, label=图10, caption=纯艏摇运动的数值模拟结果, figureFileSmall=NNpdZiLTivftX/09jQ+sIw==, figureFileBig=BaI+O/iILwKNIYUWlNMLsQ==, tableContent=null), ArticleFig(id=1242150725971685398, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=EN, label=Fig.11, caption=Predicted trajectory of catamaran turning, figureFileSmall=CE1wl4cMUOgub0BBx1dRog==, figureFileBig=09kT/zaxzKSVJle7IrlFNQ==, tableContent=null), ArticleFig(id=1242150726051377180, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=CN, label=图11, caption=双体船回转预测轨迹, figureFileSmall=CE1wl4cMUOgub0BBx1dRog==, figureFileBig=09kT/zaxzKSVJle7IrlFNQ==, tableContent=null), ArticleFig(id=1242150726135263265, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=EN, label=Tab.1, caption=

Symbolic meaning

, figureFileSmall=null, figureFileBig=null, tableContent=
符号含义符号含义
m双体船的质量XR、YR、NR舵所受纵向力、横向力和艏摇力矩
mx双体船在ox方向的附加质量X、Y、N纵向力、横向力、艏摇力矩
,v̇纵荡、横荡加速度XH、YH、NH船体所受纵向力、横向力和艏摇力矩
ṙ绕oz轴的回转角角速度XP、YP、NP螺旋桨所受纵向力、横向力和艏摇力矩
IZ双体船质量绕oz轴的转动惯量my双体船在oy方向的附加质量
), ArticleFig(id=1242150726214955047, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=CN, label=表1, caption=

符号含义

, figureFileSmall=null, figureFileBig=null, tableContent=
符号含义符号含义
m双体船的质量XR、YR、NR舵所受纵向力、横向力和艏摇力矩
mx双体船在ox方向的附加质量X、Y、N纵向力、横向力、艏摇力矩
,v̇纵荡、横荡加速度XH、YH、NH船体所受纵向力、横向力和艏摇力矩
ṙ绕oz轴的回转角角速度XP、YP、NP螺旋桨所受纵向力、横向力和艏摇力矩
IZ双体船质量绕oz轴的转动惯量my双体船在oy方向的附加质量
), ArticleFig(id=1242150726290452526, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=EN, label=Tab.2, caption=

Main parameters of catamaran

, figureFileSmall=null, figureFileBig=null, tableContent=
名称数值名称数值
船长L/m3.0设计吃水t/m0.28
型宽B/m1.5设计排水量Δ/m30.666
型深D/m0.44方形系数Cb0.528
), ArticleFig(id=1242150726407893041, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=CN, label=表2, caption=

双体船的主要参数

, figureFileSmall=null, figureFileBig=null, tableContent=
名称数值名称数值
船长L/m3.0设计吃水t/m0.28
型宽B/m1.5设计排水量Δ/m30.666
型深D/m0.44方形系数Cb0.528
), ArticleFig(id=1242150726525333563, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=EN, label=Tab.3, caption=

Working conditions of numerical simulation

, figureFileSmall=null, figureFileBig=null, tableContent=
试验漂角β/（°）振幅a/m频率f/Hz
斜拖试验0，±2，±4，±6，±800
纯横荡试验00.1,0.20.38
纯艏摇运动00.025,0.05,0.10.115
), ArticleFig(id=1242150726625996867, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=CN, label=表3, caption=

数值仿真计算工况

, figureFileSmall=null, figureFileBig=null, tableContent=
试验漂角β/（°）振幅a/m频率f/Hz
斜拖试验0，±2，±4，±6，±800
纯横荡试验00.1,0.20.38
纯艏摇运动00.025,0.05,0.10.115
), ArticleFig(id=1242150726735048776, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=EN, label=Tab.4, caption=

Research on gird convergence

, figureFileSmall=null, figureFileBig=null, tableContent=
网格划分网格数量（万）X'Y'N'
粗糙网格109.5-0.002470.02030.00210
细网格203-0.002040.01740.00198
精细网格402.3-0.002020.01690.00187
RG0.057630.663710.72031
收敛情况单调收敛单调收敛单调收敛
), ArticleFig(id=1242150726865072208, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=CN, label=表4, caption=

网格划分收敛性研究

, figureFileSmall=null, figureFileBig=null, tableContent=
网格划分网格数量（万）X'Y'N'
粗糙网格109.5-0.002470.02030.00210
细网格203-0.002040.01740.00198
精细网格402.3-0.002020.01690.00187
RG0.057630.663710.72031
收敛情况单调收敛单调收敛单调收敛
), ArticleFig(id=1242150726948958294, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=EN, label=Tab.5, caption=

Research on time step convergence

, figureFileSmall=null, figureFileBig=null, tableContent=
时间步长时间步长/sX'Y'N'
粗糙网格0.028-0.002360.02910.00221
细网格0.04-0.002040.01740.00198
精细网格0.056-0.002050.01520.00166
RT0.725390.096620.87652
收敛情况单调收敛单调收敛单调收敛
), ArticleFig(id=1242150727037038684, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=CN, label=表5, caption=

时间步长收敛性研究

, figureFileSmall=null, figureFileBig=null, tableContent=
时间步长时间步长/sX'Y'N'
粗糙网格0.028-0.002360.02910.00221
细网格0.04-0.002040.01740.00198
精细网格0.056-0.002050.01520.00166
RT0.725390.096620.87652
收敛情况单调收敛单调收敛单调收敛
), ArticleFig(id=1242150727146090596, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=EN, label=Tab.6, caption=

Hydrodynamic derivatives of the first-order model

, figureFileSmall=null, figureFileBig=null, tableContent=
水动力导数无因次值水动力导数无因次值
yv1.347×10-1nv-3.38×10-3
yr1.858×10-3nr-2.36×10-3
yv̇-2.071×10-2nv̇1.401×10-3
yṙ-3.404×10-4nṙ-2.301×10-4
), ArticleFig(id=1242150727229976683, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=CN, label=表6, caption=

一阶模型的水动力导数

, figureFileSmall=null, figureFileBig=null, tableContent=
水动力导数无因次值水动力导数无因次值
yv1.347×10-1nv-3.38×10-3
yr1.858×10-3nr-2.36×10-3
yv̇-2.071×10-2nv̇1.401×10-3
yṙ-3.404×10-4nṙ-2.301×10-4
), ArticleFig(id=1242150727301279856, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=EN, label=Tab.7, caption=

Hydrodynamic derivatives of the second-order model

, figureFileSmall=null, figureFileBig=null, tableContent=
水动力导数无因次值水动力导数无因次值
yv9.122×10-2nv3.468×10-2
y|v|v-7.096×10-1n|v|v-3.237×10-2
yv̇-2.039×10-2nv̇1.409×10-3
yr-5.201×10-4nr-3.5×10-4
yṙ1.234×10-3nṙ-1.58×10-3
y|r|r8.13×10-6n|r|r1.84×10-5
), ArticleFig(id=1242150727385165942, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=CN, label=表7, caption=

二阶模型水动力导数

, figureFileSmall=null, figureFileBig=null, tableContent=
水动力导数无因次值水动力导数无因次值
yv9.122×10-2nv3.468×10-2
y|v|v-7.096×10-1n|v|v-3.237×10-2
yv̇-2.039×10-2nv̇1.409×10-3
yr-5.201×10-4nr-3.5×10-4
yṙ1.234×10-3nṙ-1.58×10-3
y|r|r8.13×10-6n|r|r1.84×10-5
), ArticleFig(id=1242150727490023547, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=EN, label=Tab.8, caption=

Hydrodynamic derivatives of the third-order model

, figureFileSmall=null, figureFileBig=null, tableContent=
水动力导数无因次值水动力导数无因次值
yv1.036×10-1nv3.402×10-2
yvvv5.734×10-3nvvv-2.907×10-2
yv̇-2.074×10-2nv̇1.405×10-3
yr1.853×10-3nr-2.37×10-3
yṙ1.853×10-3nṙ-2.3×10-4
yrrr-3.85×10-5nrrr1.59×10-5
), ArticleFig(id=1242150727582298238, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=CN, label=表8, caption=

三阶模型水动力导数

, figureFileSmall=null, figureFileBig=null, tableContent=
水动力导数无因次值水动力导数无因次值
yv1.036×10-1nv3.402×10-2
yvvv5.734×10-3nvvv-2.907×10-2
yv̇-2.074×10-2nv̇1.405×10-3
yr1.853×10-3nr-2.37×10-3
yṙ1.853×10-3nṙ-2.3×10-4
yrrr-3.85×10-5nrrr1.59×10-5
), ArticleFig(id=1242150727666184323, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=EN, label=Tab.9, caption=

Maneuvering models of catamaran

, figureFileSmall=null, figureFileBig=null, tableContent=
双体船操纵模型方案代号船体受力模型
二阶操纵模型方案1二阶受力模型
三阶操纵模型方案2三阶受力模型
一阶二阶混合操纵模型方案3一阶模型表示艏摇力矩；二阶模型表示横向力、纵向力
一阶三阶混合操纵模型方案4一阶模型表示艏摇力矩；三阶模型表示横向力、纵向力
), ArticleFig(id=1242150729180328077, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=CN, label=表9, caption=

双体船操纵模型方案

, figureFileSmall=null, figureFileBig=null, tableContent=
双体船操纵模型方案代号船体受力模型
二阶操纵模型方案1二阶受力模型
三阶操纵模型方案2三阶受力模型
一阶二阶混合操纵模型方案3一阶模型表示艏摇力矩；二阶模型表示横向力、纵向力
一阶三阶混合操纵模型方案4一阶模型表示艏摇力矩；三阶模型表示横向力、纵向力
), ArticleFig(id=1242150729285185681, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=EN, label=Tab.10, caption=

Diameter of steady turning

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方案1方案2方案3方案4实验值
回转直径/m27.58726.19926.95026.32627.107
与实验值误差（%）1.83.30.62.8—
), ArticleFig(id=1242150729352294549, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=CN, label=表10, caption=

稳定回转直径

, figureFileSmall=null, figureFileBig=null, tableContent=
方案1方案2方案3方案4实验值
回转直径/m27.58726.19926.95026.32627.107
与实验值误差（%）1.83.30.62.8—
), ArticleFig(id=1242150729423597722, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=EN, label=Tab.11, caption=

Maneuvering parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
操纵性能5°/-5°10°/-10°15°/-15°20/-20°
回转直径/m28.22726.95026.24725.838
纵距/m2.9932.7122.5262.389
横距/m8.7498.1977.7957.483
转艏性/s76.1580.9589.16100.01
超越特性/（°）5.07765.61785.02964.4615
跟从性/s77.2777.2743.936.5
), ArticleFig(id=1242150729528455327, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1242150712109511315, language=CN, label=表11, caption=

操纵性参数

, figureFileSmall=null, figureFileBig=null, tableContent=
操纵性能5°/-5°10°/-10°15°/-15°20/-20°
回转直径/m28.22726.95026.24725.838
纵距/m2.9932.7122.5262.389
横距/m8.7498.1977.7957.483
转艏性/s76.1580.9589.16100.01
超越特性/（°）5.07765.61785.02964.4615
跟从性/s77.2777.2743.936.5
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槽道型无人双体船操纵性预报研究
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刘冬雨 , 高霄鹏 , 霍聪
船舶力学 | 流体力学 2024,28(4): 501-512
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船舶力学 | 流体力学 2024, 28(4): 501-512
槽道型无人双体船操纵性预报研究
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刘冬雨, 高霄鹏, 霍聪
作者信息
  • 海军工程大学，武汉　430000

    • 刘冬雨（1996-），女，博士研究生

    高霄鹏（1971-），女，博士，副教授

    霍聪（1989-），男，博士，副教授，通讯作者，E-mail：。

通讯作者:

通讯作者，E-mail：
Maneuverability prediction of channel-type unmanned catamarans
Dong-yu LIU, Xiao-peng GAO, Cong HUO
Affiliations
  • Naval University of Engineering, Wuhan 430000, China
出版时间: 2024-04-20 doi: 10.3969/j.issn.1007-7294.2024.04.003
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摘要
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路径规划是无人艇实现自主航行的关键技术之一，良好的路径规划方法对无人艇的智能化发展具有重要意义。而在已有的路径规划研究中，并未考虑无人艇的操纵性能。为了使规划的路径具有较短的航行时间、路径长度以及较优的路径跟踪能力，需将无人艇自身的操纵性能与路径规划算法相融合。为精确地预测船舶的操纵性能，本文以槽道型无人双体船为研究对象，通过CFD技术开展斜航、纯横荡和纯艏摇三种平面运动机构仿真试验，使用不同水动力模型对仿真结果进行拟合，计算得到相应的水动力导数。同时采用MMG模型，建立船舶操纵运动数学模型，模拟无人双体船的回转运动和Z形运动，分析不同水动力模型对仿真结果的影响，并实现无人双体船的操纵性预报。

MMG模型  /  水动力导数  /  操纵性能  /  无人双体船

Path planning is one of the key technologies for autonomous navigation of unmanned vehicles. A good path planning method is of great significance to the intelligent development of unmanned vehicles. In the existing path planning research, the maneuvering performance of unmanned vehicles is not considered. In order to make the planned path have shorter voyage time, shorter path length and better path tracking ability, it is necessary to combine the maneuvering performance of unmanned vehicles with the path planning algorithm. In order to accurately predict the ship maneuverability, the channel-type unmanned catamaran was taken as the research object, and simulation tests of three planar motion mechanisms were carried out by CFD technology. Simulation results were fitted with different hydrodynamic models, and corresponding hydrodynamic derivatives were calculated. The MMG model was used to establish a mathematical model of ship maneuvering motion to simulate the turning motion and Z-shape motion of the unmanned catamaran. The influence of different hydrodynamic models on the simulation results was analyzed, and the maneuvering pre-diction of the unmanned catamaran was realized.

MMG model  /  hydrodynamic derivative  /  maneuvering performance  /  unmanned catamaran
刘冬雨, 高霄鹏, 霍聪. 槽道型无人双体船操纵性预报研究. 船舶力学, 2024 , 28 (4) : 501 -512 . DOI: 10.3969/j.issn.1007-7294.2024.04.003
Dong-yu LIU, Xiao-peng GAO, Cong HUO. Maneuverability prediction of channel-type unmanned catamarans[J]. Journal of Ship Mechanics, 2024 , 28 (4) : 501 -512 . DOI: 10.3969/j.issn.1007-7294.2024.04.003
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0　引言
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近年来，随着人工智能的发展，世界各国在军用和民用领域加大了对无人水面艇（USV）的研究力度。基于其他无人系统成熟的研究成果，USV的研究取得了快速的发展，可实现态势感知、自主定位、自主路径规划以及自主避障等功能。自主路径规划作为无人水面艇研究领域中的关键技术，其发展水平在一定程度上影响着USV的整体发展。大多数传统的路径规划算法都将USV看作一个质点，忽略了无人艇的尺寸及其操纵性能，导致规划的路线中包含一些USV无法实现的转向点。因此，为了提高路径规划的实用性和可靠性，建立高精度的船舶操纵模型并对船舶操纵性进行预报极为重要。
目前，研究中常用的船舶操纵运动数学模型可分为响应型模型和水动力模型，水动力模型包括“整体型”和“分离型”两大类。1957年，日本学者Nomoto等[1]提出响应型模型，建立了船舶转艏角速度与舵角之间的函数关系，构建了一阶和二阶响应模型。在1967年，Abkowitz[2]提出一种整体型非线性方程，把船-桨-舵视为一个系统，将整个水动力进行泰勒级数展开。日本操纵运动模型小组[3]经多年研究，提出分离型操纵数学模型，该模型将船-桨-舵的水动力分别予以考虑，并用干扰系数表示三者之间的相互影响。
确定船舶操纵运动数学模型中的水动力导数，是实现船舶操纵性预报的关键。目前，常用的水动力导数计算方法主要有理论计算法、数值仿真计算和模型试验。理论计算法难以满足工程精度的要求；模型试验包括自航模试验和约束模试验，两者都可以精确确定船舶的水动力导数，但模型试验的成本高、耗时长，很难在设计初期实施；随着计算流体力学（CFD）在船舶领域的应用，使用数值仿真计算船舶操纵水动力导数的方法弥补了传统模型试验的不足。
在上世纪90年代以前，采用CFD预报船舶操纵性时大多基于势流理论，并将船舶模型简化，导致预报精度低。随着船舶CFD技术的发展，采用粘性流方法模拟船舶操纵运动已成为主流，主要包括两种典型方法：一是使用CFD直接展开操纵运动模拟，Mofidi等[4]以KCS为研究对象，使用CFD直接模拟其在静水域中的Z形操纵运动。Wang等[5]使用CFD开源求解器OpenFOAM研究了船舶在波浪中的Z形操纵运动。姜帆等[6]基于OpenFOAM求解器和6自由度MMG模型，对非对称双体船在不同舵角下的非定常回转运动和高舵角下的Z型运动进行了模拟仿真，实现了对该类双体船的操纵性预报。研究表明，使用CFD直接模拟船舶操纵运动的方法可以精确预测船舶操纵性，但这种方法计算成本大，并且船-桨-舵之间的耦合运动复杂，还不能成熟地应用于实际，在实际中应用更广泛的方法是使用CFD模拟船舶的拘束模试验，该方法通过在计算机上建立数值水池和船舶模型，模拟船舶的操纵运动来求解水动力导数，再结合船舶操纵运动数学模型进行操纵性预测。Sakamoto等[7]基于CFD技术和非定常雷诺平均，模拟仿真了裸型水面战斗舰5415的PMM试验，得到了与试验数据吻合度较高的水动力导数。Liu等[8]以KCS为研究对象，通过使用STAR-CCM+软件模拟拘束模试验，得到了该船模完整的线性和非线性水动力导数，并结合整体型运动模型预测了船舶的操纵性。Dai等[9]对KVLCC2开展了斜拖试验和圆周运动试验，将得到的水动力导数与分离型模型结合，模拟了船模的回转运动和Z型操纵运动。刘晨飞等[10]采用CFD和重叠网格技术，计算了KVLCC2船模在粘性流场中的操纵性水动力导数，使用MMG分离建模方法建立了船模的操纵运动模型，对船舶操纵运动进行了仿真。
尽管船舶CFD技术可以准确地模拟船舶的操纵运动，但在求解水动力导数方面仍存在较大误差，如何对模拟数据进行准确拟合，从而获得符合船舶实际的水动力导数，是建立精确船舶操纵运动数学模型的关键。本文将以某槽道型无人双体船为研究对象，采用现代船舶CFD方法对其展开斜拖、纯横荡和纯艏摇三种平面运动机构仿真试验，得到相应的水动力和力矩，对仿真数据采用最小二乘法进行拟合，求得不同拟合方案的水动力导数。最后将不同方案水动力导数与三自由度的MMG模型结合，建立不同的船舶操纵运动数学模型，借此模型预报双体船的回转运动和Z型操纵运动，将模拟轨迹与试验轨迹对比分析，从而选取最符合实际的船舶操纵运动数学模型作为后续路径规划研究的操纵模型。
1　双体船三自由度操纵运动数学模型
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1.1　建立坐标系
在外界环境的影响下，无人艇会产生六自由度的运动。为构建无人艇运动模型，首先建立两个右手直角坐标系，如图1所示。固定坐标系o1-x1y1 z1为固定在地球表面的大地坐标系，o1x1y1平面固定在静水面上，o1z1轴垂直于水面向下，双体船的航行轨迹和航行方向在此固定坐标系中表示。运动坐标系G-xyz固定在船体上，以双体船重心为原点，Gx轴平行于基平面，指向船首为正，Gy轴与纵剖面垂直，指向右舷为正，Gz轴与o1z1轴方向一致，该运动坐标系用于描述作用在双体船上的水动力以及随体坐标系下的运动参数。图1中ψ表示双体船的航向角，δ为舵角，r为艏摇角速度，u、v分别表示纵荡速度和横荡速度，双体船中心处的漂角β用式（1）表示。
1.2　船舶操纵运动数学模型
双体船在静水平面上会产生六自由度操纵运动，为了简化数学模型，本文只考虑双体船的纵荡、横荡和艏摇三自由度的运动。根据三自由度MMG模型，船舶运动方程可以表示为
式中各符号的含义在表1中列出。
1.3　船体水动力模型
船体所受粘性水动力取决于船形及其运动情况，在小扰动情况下，作用于船体的粘性水动力可以用一阶模型线性表示为
研究船舶在大舵角下的操纵运动时，需要将运动参数的非线性项加入表达式，使用三阶模型表示为
根据日本学者井上提出的非线性横向水动力模型，结合上式中的线性部分，可以将船体粘性力和力矩使用二阶模型表示为
上述各式中，双体船在直线航行时所受到的阻力用X0表示，Yv、YR、Nv、NR表示线性水动力和力矩导数，Yvvv、Yrrr、Nvvv、Nrrr表示高阶水动力导数，Yvvr、Yvrr、Nvvr、Nvrr表示高阶耦合水动力导数。
1.4　舵受力模型
双体船在操纵运动中，舵受到的力可以用方程式表示：
式中，tR表示阻力减额系数，xR表示舵的纵向位置，αH是舵对船体水动力的影响系数。由于转舵会引起船体周围压力场的变化，使船体产生横向力，xH即表示该力作用点的纵坐标。FN表示舵法向力，可以用式（8）表示为
式中，AR表示舵的有效面积，VR表示舵的有效来流速度，αR是来流有效冲角，λ为舵的展舷比，ρ是水的密度。
1.5　螺旋桨受力模型
螺旋桨受到的纵向力XP可表示为
式中，tP表示推力减额系数，nP是螺旋桨的转速，DP表示螺旋桨的直径，JP表示螺旋桨的推进系数，KT表示推力系数，可以用推进系数的二阶多项式表示，wP为伴流系数。
2　数值计算模型
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2.1　计算方法
本文采用CFD仿真软件STAR-CCM+进行模拟数值计算。在模拟船体周围流场时，认为流场是不可压缩的粘性流场，可用连续性方程和雷诺平均方程表示为
式中，ui为平均速度分量，P为平均压力，μ为流体分子动力粘性系数，为雷诺应力项。
在求解分离和复杂二次流特征流动时，采用Realizable k-ε湍流模型进行RANS方程的封闭。时间项采用隐式非定常，流场材质使用欧拉多相流。采用VOF模型处理自由液面，通过设置VOF模型的参数，定义流体密度、船体航速和自由液面的位置等。
2.2　计算对象
本文的研究对象为一槽道型无人双体船，由于船体本身规模较小，直接等比例建立三维计算模型，其几何形状如图2所示。该双体船的主要参数如表2所示。
2.3　模拟平面运动机构运动状态的计算模型
为了获得准确的槽道型无人双体船的水动力导数，本文应用CFD技术，对双体船的无螺旋桨无舵模型展开了斜航运动、纯横荡运动和纯艏摇运动的仿真模拟，图3分别给出了三种模拟的运动方式。
所有模拟计算都是在船舶运动受限的静态条件下进行的。在算例中设置模拟船速为2 m/s，表3列出了本文所有计算工况。在运动模拟过程中，需要对双体船所受到的纵向力X、横向力Y和艏摇力矩N进行监测。
2.4　计算域和网格
数值计算域的选取如图4所示，进水口设置在双体船船首前方1.5L处，出水口位于船尾后方3.0L处，顶部位于自由水面上方1.0L处，底部位于2.0L处，左右两侧分别位于距离左舷和右舷1.0L处。对于边界条件，将出水口平面设置为压力出口，将船体表面设置为无滑移壁面，其余各边界均设置为速度入口。
计算域采用非结构化六面体网格，为了准确获取船舶运动过程中的流体特性，对双体船周围和自由液面周围的网格进行了加密处理；同时为了节约时间和计算资源，对远离船体的区域采用稍稀疏的网格，如图4所示。
2.5　收敛性分析
本文以β = 8°、v = 2 m/s的斜航试验为例，采用Stern等[11]和Wilson等[12]的验证方法，研究了网格划分和时间步长对计算结果的影响。在网格划分收敛性的研究中，所有网格参数都是以基本尺寸的百分比给出，以便对网格进行系统的细化。基于细化比选取了三种网格划分方案，分别为109.5万的粗糙网格、203万的细网格和402.3万的精细网格。在时间步长均为0.04 s的情况下，计算时间分别为18 h、35 h和62 h。在对时间步长进行收敛性研究时，采用203万的网格划分方案进行仿真模拟。基于时间步长划分比例设置三种时间步长方案：0.028 s、0.04 s和0.056 s。不同方案下的研究结果分别如表4和表5所示。根据表4可以看出：在网格划分收敛研究中，X'、Y'和N'均满足0 < RG < 1，达到单调收敛。同样，在时间步长收敛分析中，X'、Y'和N'均满足0 < RT < 1，达到单调收敛，如表5所示。因此综合考虑研究精度和计算时间，在后续仿真模拟中，选取203万网格的细网格划分方案和0.04 s的时间步长方案。
3　数值模拟结果与分析
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3.1　斜航运动计算结果
双体船的模拟航速为2 m/s，经过系统改变漂角，可以得到不同侧向速度下双体船受到的纵向力X、侧向力Y和艏摇力矩N。在模拟仿真中，当漂角分别为-2°和-8°时，船体周围的兴波如图5所示。由兴波图可知：随着漂角的增加，船体两侧的兴波越来越不对称，背流面散出的波形距离船体越来越远。
使用不同的水动力数学模型对数值计算结果进行拟合，得到横向力和艏摇力矩随侧向速度的变化曲线如图6所示。由图可知，三种水动力模型的拟合曲线变化趋势基本一致，拟合效果良好。根据仿真数据可以得到以下结论：
（1）随着漂角的增大，双体船所受的横向力和艏摇力矩也随之增大；
（2）漂角为8°时船体所受的横向力大于漂角为-8°时船体受到的横向力，在其余工况下，正漂角和负漂角时船体受力基本相等，说明该双体船在大漂角的情况下会出现横向受力左右不对称的情况。
3.2　纯横荡运动计算结果
双体船在纯横荡运动时，其运动方式为在纵向匀速运动的基础上叠加一横向的简谐运动，运动规律为
式中，a表示振幅，ω表示双体船运动的圆频率。
在模拟速度为2 m/s的工况下，本文分别计算了振幅为0.1 m和0.2 m时双体船的纯横荡运动。船体周围的兴波云图如图7所示。由图可知，随着振幅的增大，船体两侧的兴波会出现不对称的情况。
在整个计算过程中选取两个稳定周期的数值结果进行分析。通过使用不同的水动力模型对双体船的仿真数据进行拟合，得到双体船受到的横向力和艏摇力矩的时历曲线如图8所示。根据数据拟合结果，可以得到以下结论：
（1）双体船在纯横荡运动过程中，随着振动幅度的增大，船体所受到的横向力和艏摇力矩也随之增大；
（2）虽然二阶模型的拟合曲线符合简谐运动的规律，但是拟合曲线不够平滑，相比于一阶模型和三阶模型，其拟合效果较差。
3.3　纯艏摇运动计算结果
纯艏摇运动是在纯横荡运动的基础上叠加一个首向角的周期变化，如式（12）所示，式中r表示双体船艏摇角速度，V表示双体船的运动速度。
在纯艏摇运动的仿真中，设置航速V = 2 m/s，振幅分别为0.05 m、0.1 m；纯艏摇运动过程中船体两侧的兴波云图如图9所示。由图可知，两种振幅下，船体周围的兴波云图左右对称。
在整个计算过程中选取一个稳定周期的数值结果进行分析，使用三种水动力模型对数值仿真结果进行拟合，得到双体船的横向力和艏摇力矩的时历曲线如图10所示。图中，左侧两图的模拟工况为：振幅为0.1 m、频率为0.115 Hz；右侧两图的模拟工况为：振幅0.05 m、0.025 m，频率0.38 Hz。根据拟合结果可以得知，在振幅为0.1 m、频率为0.115 Hz的运动情况下，双体船受到的横向力不能很好地符合简谐运动的规律，三种水动力模型的拟合效果都不能真实反映船体的实际受力情况；为了对比效果，又仿真了振幅为0.1 m、频率为0.38 Hz的纯艏摇运动，测得的横向力符合简谐运动规律，三种水动力模型的拟合效果也较好。
3.4　水动力导数计算结果
根据三种水动力模型的拟合结果，计算得到每种模型下的船体水动力导数，分别如表6~8所示。得到的水动力导数将用于建立双体船的操纵运动数学模型，以仿真船舶的实际运动轨迹并预测双体船的操纵性能。
4　操纵性预测
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为了对比分析水动力模型与实船的吻合度，本文将通过CFD仿真获得的水动力导数与MMG操纵模型结合，模拟双体船的回转运动和Z形运动，将模拟得到的运动轨迹与实船试验轨迹进行分析，选出误差最小的模型方案，从而确定该双体船的操纵运动数学模型。在使用MMG模型预测操纵性时，螺旋桨和舵的相关参数通过回归方法估算。船体受力分别使用前文所述三种不同的受力模型进行表示，从而得到不同的双体船操纵模型，如表9所示。分别使用四种操纵模型模拟双体船的回转运动，舵角为-10°的回转运动轨迹如图11所示，计算回转直径如表10所示。综合分析回转轨迹与回转直径，发现方案3操纵模型的模拟轨迹与实船试验轨迹拟合程度最高，回转直径与实验值误差最小，故选取方案3的模型作为该槽道型双体船的运动学模型。根据该模型的模拟试验，预测了该双体船的回转直径、纵距、横距、转艏性、跟从性以及超越特性，如表11所示。转艏性表征着双体船的航向角变化指定角度所需时间；超越特性表征着双体船在反向操舵后继续增加的角度，跟从性表征着双体船转艏加速度消失，进入稳定新航向所需时间。对这些性能进行准确预测，并将其融入路径规划的算法中，不仅为路径规划提供一种新的思路，还将会得到更加符合无人艇操纵性能的路径。
5　结论
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本文基于CFD仿真技术，以既可自主航行、又可遥控操纵的槽道型双体船的裸船体为研究对象，建立了船舶三自由度运动方程，并开展了斜航、纯横荡和纯艏摇三种PMM运动模拟试验，计算出相应条件下的水动力和力矩，对计算结果使用不同受力模型处理后得到相应的操纵水动力导数。应用得到的水动力导数建立不同的双体船操纵运动数学模型，根据实船试验轨迹对不同模型的精确度作出评价，选择与实船试验拟合度最高的操纵模型用于后续深入研究，并使用该模型对该双体船的回转运动和Z形运动进行仿真，得到无人双体船的回转半径、转艏性以及跟从性等操纵性信息，初步掌握了该槽道型无人双体船的操纵性能，为路径规划的优化研究奠定了基础。通过计算与分析，可以得到以下结论：
（1）本文采用的船体水动力的展开方式可以更好地贴合实船实验数据，据此建立的数学模型具有更高的精度；
（2）由槽道型无人双体船在斜航角度为0°（直航）时的水动力计算结果可知，其阻力值较小，这是由于在航行过程中，空气从艇首部槽道口处进入，形成的空气层可以起到对槽道顶面的润滑降阻作用；
（3）由于槽道型无人双体船底部的刚性侧壁和中心排水体的存在，使得其在回转运动中侧滑较小，从而具有较小的回转直径。
基金
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  • 舰载水面无人船型技术研究(20190190)
文献
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参考文献 引证文献
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2024年第28卷第4期
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doi: 10.3969/j.issn.1007-7294.2024.04.003
  • 接收时间：2023-10-24
  • 首发时间：2026-03-21
  • 出版时间：2024-04-20
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  • 收稿日期：2023-10-24
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舰载水面无人船型技术研究(20190190)
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    海军工程大学，武汉　430000

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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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