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Article(id=1243253930495427250, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243253924128469739, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2025.07.007, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1737216000000, receivedDateStr=2025-01-19, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774344435571, onlineDateStr=2026-03-24, pubDate=1752940800000, pubDateStr=2025-07-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774344435571, onlineIssueDateStr=2026-03-24, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774344435571, creator=13701087609, updateTime=1774344435571, 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=1078, endPage=1088, ext={EN=ArticleExt(id=1243253930847748797, articleId=1243253930495427250, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Numerical study on interference characteristics of multiple two-element wingsails on sail-assisted ships, columnId=1241023037940748650, journalTitle=Journal of Ship Mechanics, columnName=Hydrodynamics, runingTitle=null, highlight=null, articleAbstract=

In order to study the interference characteristics between multiple wingsails on sail-assisted vessels during navigation, a lateral arrangement scheme of a two-element wingsail based on the relative wind direction angle was designed. The Reynolds averaged N-S equation was used for numerical simulation under steady conditions. The aerodynamic interference performance of the two-element wingsail was analyzed, and an optimization scheme for the angle of attack and flap deflection angle was proposed to address the stall problem caused by the interference of multi-sails. Furthermore, the interstage interference characteristics of wingsails were obtained. The results show that, in the single row arrangement scheme, the optimal spacing is 1.5c for relative wind angles of 30°, 90°, and 120°. However, the interstage interference can cause the wingsail to stall at the relative wind angles of 90° and 120°. After optimization, the auxiliary thrust coefficient can be increased by more than 5.2%, and the flow separation on the downstream wingsail disappears.

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为了研究风帆助航船舶在航行中多组翼帆之间的干涉特性，本文首先基于相对风向角设计了双元素翼帆相邻布置方案，并采用雷诺平均N-S方程在定常工况下进行数值仿真，以分析双元素翼帆的气动干涉特性，针对多帆干涉引起的失速问题，提出了一种优化双元素翼帆攻角和襟翼偏转角的方案，并据此获得了翼帆级间干涉特性。研究结果表明，在单排布置方案中，当相对风向角为30°、90°和120°时，最佳间距均为1.5c，但当相对风向角为90°和120°时，级间干涉显著增强从而引起翼帆失速，经优化后，双元素翼帆系统的助推力系数可提升5.2%以上，下游翼帆的流动分离消失。

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李臣（1988-），男，博士、副教授，E-mail：。

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李臣（1988-），男，博士、副教授，E-mail：。

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李臣（1988-），男，博士、副教授，E-mail：。

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ArticleFig(id=1243253941127987415, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253930495427250, language=EN, label=Tab.1, caption=

Parameterization of the wingsail

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参数取值
总弦长c3.5 m
襟翼弦长比c2/c0.4
襟翼偏转角δ0~25°
缝隙相对宽度g2.4%
襟翼旋转轴位置Xr90%
), ArticleFig(id=1243253941232845017, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253930495427250, language=CN, label=表1, caption=

翼帆的参数设置

, figureFileSmall=null, figureFileBig=null, tableContent=
参数取值
总弦长c3.5 m
襟翼弦长比c2/c0.4
襟翼偏转角δ0~25°
缝隙相对宽度g2.4%
襟翼旋转轴位置Xr90%
), ArticleFig(id=1243253941346091230, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253930495427250, language=EN, label=Tab.2, caption=

Configurations for initial angle of attack and flap deflection angle of two-element wingsails

, figureFileSmall=null, figureFileBig=null, tableContent=
相对风向角翼帆参数Wingsail01Wingsail02Wingsail03
30°δ/(°)555
α/(°)888
90°δ/(°)252525
α/(°)121212
120°δ/(°)151515
α/(°)101010
), ArticleFig(id=1243253941467726051, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253930495427250, language=CN, label=表2, caption=

双元素翼帆的初始攻角和襟翼偏转角配置方案

, figureFileSmall=null, figureFileBig=null, tableContent=
相对风向角翼帆参数Wingsail01Wingsail02Wingsail03
30°δ/(°)555
α/(°)888
90°δ/(°)252525
α/(°)121212
120°δ/(°)151515
α/(°)101010
), ArticleFig(id=1243253941593555176, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253930495427250, language=EN, label=Tab.3, caption=

Spacing of two-element wingsail on ship

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间距方案Case 1Case 2Case 3
间距大小1c1.5c2c
), ArticleFig(id=1243253941752938734, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253930495427250, language=CN, label=表3, caption=

双元素翼帆在船横向间距布置方案

, figureFileSmall=null, figureFileBig=null, tableContent=
间距方案Case 1Case 2Case 3
间距大小1c1.5c2c
), ArticleFig(id=1243253941887156467, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253930495427250, language=EN, label=Tab.4, caption=

Propulsion performance of the wingsails at θ=30° for Case 1, Case 2 and Case 3

, figureFileSmall=null, figureFileBig=null, tableContent=
翼帆间距方案翼帆编号CLCDCXCY
Case 1Wingsail012.085-0.0911.1221.761
Wingsail020.8720.1200.3320.815
Wingsail030.3980.0760.1340.383
平均值1.1200.0350.5290.986
Case 2Wingsail011.839-0.0570.9691.565
Wingsail021.0390.0820.4490.941
Wingsail030.6180.0790.2410.575
平均值1.1660.0350.5551.027
Case 3Wingsail011.644-0.0340.8511.407
Wingsail021.0970.0590.4970.981
Wingsail030.7540.0730.3130.689
平均值1.1650.0330.5531.025
), ArticleFig(id=1243253942000402678, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253930495427250, language=CN, label=表4, caption=

相对风向角为30°时不同间距方案下的翼帆推进性能

, figureFileSmall=null, figureFileBig=null, tableContent=
翼帆间距方案翼帆编号CLCDCXCY
Case 1Wingsail012.085-0.0911.1221.761
Wingsail020.8720.1200.3320.815
Wingsail030.3980.0760.1340.383
平均值1.1200.0350.5290.986
Case 2Wingsail011.839-0.0570.9691.565
Wingsail021.0390.0820.4490.941
Wingsail030.6180.0790.2410.575
平均值1.1660.0350.5551.027
Case 3Wingsail011.644-0.0340.8511.407
Wingsail021.0970.0590.4970.981
Wingsail030.7540.0730.3130.689
平均值1.1650.0330.5531.025
), ArticleFig(id=1243253942138814715, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253930495427250, language=EN, label=Tab.5, caption=

Adjustment schemes of Wingsail01, Wingsail02 and Wingsail03 at θ=90°

, figureFileSmall=null, figureFileBig=null, tableContent=
参数翼帆编号Structure AStructure BStructure CStructure D
襟翼偏转角δ/(°)Wingsail0125211919
Wingsail0225211919
Wingsail0325211919
攻角α/(°)Wingsail0110101214
Wingsail0210101214
Wingsail0310101214
), ArticleFig(id=1243253942235283710, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253930495427250, language=CN, label=表5, caption=

相对风向角为90°时各组翼帆的调整方案

, figureFileSmall=null, figureFileBig=null, tableContent=
参数翼帆编号Structure AStructure BStructure CStructure D
襟翼偏转角δ/(°)Wingsail0125211919
Wingsail0225211919
Wingsail0325211919
攻角α/(°)Wingsail0110101214
Wingsail0210101214
Wingsail0310101214
), ArticleFig(id=1243253942335947011, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253930495427250, language=EN, label=Tab.6, caption=

Propulsion performance of two-element wingsails of adjustment scheme of Structure C

, figureFileSmall=null, figureFileBig=null, tableContent=
调整方案翼帆编号CLCDCXCY
Structure CWingsail012.9150.0712.9160.071
Wingsail022.0430.0752.0430.075
Wingsail031.5530.0561.5530.056
平均值2.1710.0672.1710.067
), ArticleFig(id=1243253942411444486, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253930495427250, language=CN, label=表6, caption=

Structure C方案的双元素翼帆的推进性能

, figureFileSmall=null, figureFileBig=null, tableContent=
调整方案翼帆编号CLCDCXCY
Structure CWingsail012.9150.0712.9160.071
Wingsail022.0430.0752.0430.075
Wingsail031.5530.0561.5530.056
平均值2.1710.0672.1710.067
), ArticleFig(id=1243253942503719183, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253930495427250, language=EN, label=Tab.7, caption=

Angle-of-attack adjustment of wingsails for Case 2 at θ=120°

, figureFileSmall=null, figureFileBig=null, tableContent=
参数翼帆编号Structure AStructure BStructure C
攻角/(°)Wingsail01121212
Wingsail02101212
Wingsail03101012
), ArticleFig(id=1243253942608576790, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253930495427250, language=CN, label=表7, caption=

相对风向角为120°时各组翼帆的攻角调整方案（间距方案Case 2）

, figureFileSmall=null, figureFileBig=null, tableContent=
参数翼帆编号Structure AStructure BStructure C
攻角/(°)Wingsail01121212
Wingsail02101212
Wingsail03101012
), ArticleFig(id=1243253942696657181, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253930495427250, language=EN, label=Tab.8, caption=

Propulsion performance of two-element wingsail adjusted by Structure B

, figureFileSmall=null, figureFileBig=null, tableContent=
攻角方案翼帆编号CLCDCXCY
Structure BWingsail012.1640.2041.976-0.905
Wingsail021.860.0741.648-0.866
Wingsail031.614-0.0341.38-0.836
平均值1.8790.0811.668-0.869
), ArticleFig(id=1243253942797320481, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253930495427250, language=CN, label=表8, caption=

Structure B方案中双元素翼帆的推进性能

, figureFileSmall=null, figureFileBig=null, tableContent=
攻角方案翼帆编号CLCDCXCY
Structure BWingsail012.1640.2041.976-0.905
Wingsail021.860.0741.648-0.866
Wingsail031.614-0.0341.38-0.836
平均值1.8790.0811.668-0.869
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风帆助航船舶双元素翼帆多帆干涉特性的数值研究
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李臣 1, 2, 3 , 王宏明 1
船舶力学 | 流体力学 2025,29(7): 1078-1088
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船舶力学 | 流体力学 2025, 29(7): 1078-1088
风帆助航船舶双元素翼帆多帆干涉特性的数值研究
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李臣1, 2, 3 , 王宏明1
作者信息
  • 1.江苏海事职业技术学院机　电学院，南京　211170
  • 2.大连海事大学　轮机工程学院，辽宁　大连　116026
  • 3.江苏船舶节能减排工程技术研究开发中心，南京　211170

    • 李臣（1988-），男，博士、副教授，E-mail：。

Numerical study on interference characteristics of multiple two-element wingsails on sail-assisted ships
Chen LI1, 2, 3 , Hong-ming WANG1
Affiliations
  • 1.College of Marine, Electrical and Intelligent Engineering, Jiangsu Maritime Institute, Nanjing 211170, China
  • 2.Marine Engineering College, Dalian Maritime University, Dalian 116026, China
  • 3.Jiangsu Ship Energy Saving Engineering Technology Center, Nanjing 211170, China
出版时间: 2025-07-20 doi: 10.3969/j.issn.1007-7294.2025.07.007
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摘要
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为了研究风帆助航船舶在航行中多组翼帆之间的干涉特性，本文首先基于相对风向角设计了双元素翼帆相邻布置方案，并采用雷诺平均N-S方程在定常工况下进行数值仿真，以分析双元素翼帆的气动干涉特性，针对多帆干涉引起的失速问题，提出了一种优化双元素翼帆攻角和襟翼偏转角的方案，并据此获得了翼帆级间干涉特性。研究结果表明，在单排布置方案中，当相对风向角为30°、90°和120°时，最佳间距均为1.5c，但当相对风向角为90°和120°时，级间干涉显著增强从而引起翼帆失速，经优化后，双元素翼帆系统的助推力系数可提升5.2%以上，下游翼帆的流动分离消失。

风帆助航船舶  /  双元素翼帆  /  多组翼帆  /  干涉特性  /  数值模拟

In order to study the interference characteristics between multiple wingsails on sail-assisted vessels during navigation, a lateral arrangement scheme of a two-element wingsail based on the relative wind direction angle was designed. The Reynolds averaged N-S equation was used for numerical simulation under steady conditions. The aerodynamic interference performance of the two-element wingsail was analyzed, and an optimization scheme for the angle of attack and flap deflection angle was proposed to address the stall problem caused by the interference of multi-sails. Furthermore, the interstage interference characteristics of wingsails were obtained. The results show that, in the single row arrangement scheme, the optimal spacing is 1.5c for relative wind angles of 30°, 90°, and 120°. However, the interstage interference can cause the wingsail to stall at the relative wind angles of 90° and 120°. After optimization, the auxiliary thrust coefficient can be increased by more than 5.2%, and the flow separation on the downstream wingsail disappears.

sail-assisted ships  /  two-element wingsail  /  multiple sails  /  interference characteristics  /  numerical simulation
李臣, 王宏明. 风帆助航船舶双元素翼帆多帆干涉特性的数值研究. 船舶力学, 2025 , 29 (7) : 1078 -1088 . DOI: 10.3969/j.issn.1007-7294.2025.07.007
Chen LI, Hong-ming WANG. Numerical study on interference characteristics of multiple two-element wingsails on sail-assisted ships[J]. Journal of Ship Mechanics, 2025 , 29 (7) : 1078 -1088 . DOI: 10.3969/j.issn.1007-7294.2025.07.007
正文
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0　引言
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硬质翼帆是一种新型的无动力帆船推进装置，由于其环保节能的特点，开始在各类大型船舶上应用[1-2]。在翼帆研究中，由于单翼帆升力系数和失速特性的限制，单个翼帆通常很少被直接应用到风帆设计中。为了提升翼帆的推进性能国内外设计者先后对翼帆进行优化设计，从而出现了一系列的新型翼帆，如双元素翼帆、三元素翼帆等。其中双元素翼帆通过控制在翼型吸力面的气体流动方向，延缓流动分离，从而提升翼帆的推进性能。同时，为了充分利用甲板空间以提升推进性能，通常在船舶甲板上布置多组风帆。2018年，中国大船集团交付的超大型原油船（VLCC）“凯立”轮，安装有两台翼型风帆，试航结果显示，“凯立”轮风帆节能效果明显[3]。然而，由于两台翼帆的距离较近，上游翼帆与下游翼帆的流场可能会互相干涉[4]，引起翼帆表面出现流动分离或失速现象，从而降低翼帆的推进性能。因此，开展风帆助航船舶翼帆的多帆干涉特性研究具有十分重要的意义。
为此，许多学者对风帆助航船舶的多帆干涉特性开展了相关研究。Fujiwara等[5-7]对新型组合式帆的多帆干涉影响开展了相关数值研究，评估了该帆-帆相互作用以及帆-船体相互作用对实际帆安装位置的影响。实验表明，对于额定航速为13.5 kn的散货船，这种组合式帆在平行位置安装矩形风帆比在渐进排列位置安装时，其平均驱动力损失达7%，而三角形帆则达5%，可见，帆-船相互位置对帆在船上的布置位置影响较大。Jo等[8]以多组翼帆的最大平均推力系数为优化目标，采用遗传算法和代理模型对翼帆的九个设计变量进行优化设计，并通过CFD数值仿真分析翼帆的空气动力学特性，其中翼帆相对风向角的允许范围在45°~135°之间。优化后的多排翼帆与初始的多排翼帆模型相比，平均推力性能在所有风向上均得到改善，总体推力性能获得9%~11%的提升。在国内，张天逸[9]、胡以怀等[10]选用圆弧型翼帆作为目标船舶的风帆，研究了风帆间距、来风方向及两帆旋转角度对目标船推进性能的影响，分析了风帆干涉对升阻力系数的影响，获得了多帆的级间干涉效应。司朝善等[11]分析了不同风向角时各帆之间的气动干涉现象，并通过试验研究了多帆组合体的帆距对提升多帆组合体推力的效果，为双元素翼帆的在船干涉效应提供了很好的借鉴。Qiao等[12]对主翼改型的可变拱角帆（VCS）的推进性能进行了数值仿真和实验验证，重点研究了风向角在30°~150°范围内三个风帆之间的气动干涉作用，结果表明，推力系数随着帆距的增加而增大，帆距过小会增加气动相互作用，在上游翼帆尾流的干扰作用下会引起下游翼帆发生失速现象。在船舶甲板上布置多组风帆确实可以充分利用甲板空间，提升总体推力性能，提高节能效果，但应充分考虑到多帆布置时多帆干涉可能引起的下游翼帆流动分离加剧及失速提前发生的问题。
为了更好地了解双元素翼帆在不同横向间距下的干涉特性，本文基于相对风向角设计了多种双元素翼帆横向间距布置方案，对双元素翼帆的气动干涉性能进行了数值模拟，针对多帆干涉引起的失速问题，提出了一种优化的双元素翼帆的攻角和襟翼偏转角方案，获得了翼帆级间干涉特性。
1　物理模型与数值方法
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1.1　双元素翼帆翼型模型和布置方案
本文的研究对象是基于Daniel[13]研究的三元素翼帆的主翼和襟翼组成的双元素翼帆[14]，双元素翼帆叶片几何截面由主翼为NACA0018翼型和襟翼为NACA0015翼型组成，如图1所示。其中，双元素翼帆翼型的总弦长（c）、襟翼弦长比（c2/c）、襟翼偏转角（δ）、襟翼旋转轴位置（Xr）以及缝隙相对宽度（g）等参数的配置方案如表1所示[15]。
为了开展单排布置方案对双元素翼帆翼型气动性能的影响研究，本文将单排多组翼帆中相邻双元素翼帆之间的距离定义为翼帆间距，其大小以双元素翼帆总弦长的倍数表示。通过调整间距大小，保证船舶获得稳定高效的风帆推进力。对于单排双元素翼帆，将最靠近甲板上层建筑的这组双元素翼帆命名为Wingsail01，其余依次为Wingsail02和Wingsail03，如图2所示。根据不同风向角时双元素翼帆在船布置策略[16]和双元素翼帆的结构特点[17]，提出了双元素翼帆在不同相对风向角的初始攻角和襟翼偏转角的配置方案，如表2所示。但由于受到翼帆级间气动干涉的影响，Wingsail02和Wingsail03在不同相对风向角时的最优攻角和襟翼偏转角需要调整。
在进行双元素翼帆的单排布置研究时，本文以三组双元素翼帆为例，首先探讨了相对风向角为30°时的不同间距方案，再依次分析了相对风向角为90°、120°时单排布置方案的干涉特性。横向间距确定后，通过调节Wingsail02和Wingsail03的来流攻角和襟翼偏转角，来获得各组双元素翼帆在不同相对风向角的最佳配置。单排双元素翼帆间距布置方案如表3所示。
1.2　计算域和网格
根据图1中双元素翼帆翼型的结构特点，确定了如图3所示的二维数值计算域。为了避免计算域边界对双元素翼帆翼型外流场的影响，取翼型前方长度为12c，翼型后方长度为20c，宽度为12c，形成一个32c×24c的长方形计算域。计算域前后边界和下边界设置为速度进口，来流湍流强度为1%，湍流黏度比为7，由于湍流模型选择Transition SST模型，全湍流状态时间歇因子设置为1；出口边界设置为压力出口，总压为101 325 Pa；翼型壁面设置为无滑移固壁条件。
在CFD计算中，网格质量决定了数值计算的精度和效率。采用ANSYS ICEM非结构化网格对计算域二维模型进行网格划分，并对缝隙网格进行了细化加密。为了满足湍流模型对边界层模拟的要求，需确保壁面y+小于等于1[18]，因此设置翼帆面的第一层网格高度设为0.85×10−5c，边界层的增长率为1.05，边界层层数为20，网格总数约为1.24×106。
1.3　网格独立性检查
为了保证网格数量对双元素翼帆翼型的气动特性不产生影响，分别采用Transition SST湍流模型对四种不同的网格数（6.3×105、9.5×105和1.24×106、1.54×106）进行模拟准确度评估。图4为襟翼偏转角为0°的Case 3方案在Re=2.4×106时Wingsail01翼型的升力系数和阻力系数。从图4中可以看出，阻力系数随网格数的增加基本不变，升力系数随网格数的增加稍有波动，但波动范围在0.5%以内，满足数值计算要求，考虑到网格数过多带来的计算成本增加，本文二维模型计算域采用的网格数为1.24×106。
为了进一步验证网格可靠性，还分析了Transition SST湍流模型在Re=2.4×106时网格尺寸对边界层转捩的影响，如图5所示。从图5可以看到，在网格数为1.24×106和1.54×106的网格结果中，主翼压力面上有一段明显的层流分离气泡，而对于网格数为6.3×105和9.5×105的网格没有明显的层流分离气泡。在网格数为1.24×106和1.54×106之间，翼型边界层分离泡的位置和大小基本一致。因此，1.24×106的网格数适合于研究双元素翼帆翼型的气动干涉特性。
1.4　模型验证
在对双元素翼帆翼型进行仿真求解之前，需要对数值模拟方法进行基础性验证。本文在双元素翼帆翼型计算中，选择经典的NACA0018翼型为计算对象，对采用Transition SST湍流模型来预测性能和捕捉流场信息的准确性进行验证。荷兰代尔夫特大学风洞实验室[19]曾针对NACA0018翼型在中低雷诺数时的气动性能进行了全攻角范围实验，并获得了较为详实的升阻特性的实验数据。为了保证本文数值仿真方法的准确性，采用代尔夫特大学风洞实验室的NACA0018翼型的实验数据对本文的数值方法进行模型验证，其网格类型要求与双元素翼帆翼型模型相同。
图6比较了雷诺数为1.6×105时NACA0018翼型升力和阻力系数的实验数据[20]与数值结果对比。从图中可以看出，Transition SST湍流模型计算所得的升力系数、阻力系数值与实验数据均吻合较好，当攻角较大时，实验的升力系数略低于数值模拟的升力系数，而阻力系数也出现波动，这是因为攻角增大后，翼型边界层对转捩过程的气流分离有很大影响，这又与气流的湍流度、表面粗糙度等参数有关。同时Transition SST湍流模型由于加入了额外的两个变量运输方程，能够捕捉边界层转捩过程，其计算结果也接近实验值。这说明本文采用的数值模拟方法在预测翼型气动性能方面是比较准确的。
图7为α=0°时，Transition SST湍流模型与Nakano[21]实验结果中的层流分离泡位置的匹配情况。从图中可以看出，Transition SST湍流模型预测NACA0018翼型层流分离点的位置在0.512倍弦长（S点）位置，再附着点在0.78倍弦长（RA）位置，尽管Nakano的实验结果中的相对弦长较数值模拟结果大，但其测得的NACA0018翼型边界层分离点（S点）以及再附着点（RA）位置，基本与Transition SST湍流模型预测结果一致，这说明采用Transition SST湍流模型来预测层流分离泡和边界层转捩位置比较准确。
2　单排双元素翼帆的气动干涉特性分析
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升阻系数和推进系数是衡量翼帆推进性能的重要无量纲参数，为直观理解双元素翼帆翼型的升阻系数和推进系数，本文对其在船模型进行受力分析[2]，如图8所示。其中，x轴正向为船首方向，y轴正向为船舶右舷方向，相对船舶的风速记为ν0，来风方向与船首的夹角定义为相对风向角，用θ表示，如果是船首方向来风则相对风向角为0°，且沿着俯视船舶的逆时针方向增大，船尾方向来风则相对风向角为180°。翼帆受到的升力为FL，阻力为FD，将翼帆升力和阻力进行合成分解，得到沿着船舶航向的助推力Fx和垂直于船舶航向的侧推力FY。船舶翼帆的助推力系数CX和侧推力系数CY分别为
式中，θ为相对风向角。
2.1　相对风向角为30°时的干涉特性
为了分析相对风向角为30°时多组双元素翼帆相邻排列时的干涉特性，表4列出了雷诺数为2.4×106时不同横向间距下各组双元素翼帆的推进性能，图9为θ=30°时三组双元素翼帆在不同间距方案下的静压云图。从表4可以看出，Case 2和Case 3总体性能较为接近，平均升力系数较Case 1提升了4.1%，平均助推力系数提升了4.9%，而侧推力系数也有所增加，但其平均值仍小于1.1，满足设计要求。在每一种布置方案的三组翼帆中，都是Wingsail01的升力系数最大，其阻力系数则皆为负值，而Wingsail03的升力系数皆为最小，这是受相邻两组双元素翼帆流场干涉作用的影响，如图9所示。
从图9（a）中可以看出，Wingsail01的负压最大，而Wingsail03几乎没有负压。在Case 1中，正压在三组双元素翼帆之间未被分开，由于双元素翼帆的间距较小，上游双元素翼帆的正压对下游双元素翼帆吸力面的负压产生干涉效应，降低了下游双元素翼帆的升力。从图9（b）和（c）中可以看出，随着翼帆间距的增大，Wingsail01的负压减小，Wingsail02和Wingsail03的负压增大，这与表4中升力系数的变化规律一致，Wingsail01的尾缘到Wingsail02的前缘之间的压力趋向于0，表明上游双元素翼帆对下游双元素翼帆吸力面负压的干涉作用减弱，在图9（c）中几乎不存在这种级间干涉效应。
图10给出了相对风向角为30°时三种间距方案下的双元素翼帆速度云图，从图10（a）中也可以看出Wingsail01对Wingsail02来流流速的干涉作用，Wingsail02前缘的来流流速明显降低，这就限制了Wingsail02的升力系数，而图10（b）和（c）中则不存在这种现象。
2.2　相对风向角为90°时的干涉特性
2.2.1　不同横向间距的影响
为了分析相对风向角为90°时多组双元素翼帆相邻排列时的干涉特性，图11列出了相对风向角为90°时不同横向间距方案的三组双元素翼帆的性能对比。从图11可以看出，在三种间距方案中Case 2的助推力系数最大达1.85，而侧推力系数平均值仅有0.223，满足设计要求，这与相对风向角为30°时间距方案的最优选择一致。但是，通过对比其阻力系数以及图12可以发现，在Case 1、Case 2和Case 3三种方案中，由于多组双元素翼帆级间的干涉效应，襟翼吸力面发生了流动分离，导致双元素翼帆发生失速，而在相同攻角和襟翼偏转角下的单组双元素翼帆（如图12（a））并未存在流动分离现象。这就需要对多组双元素翼帆的失速机理和影响规律开展研究，在级间存在干涉作用时对各组双元素翼帆的攻角或襟翼偏转角进行调整，以保证各组双元素翼帆在不失速状态下的安全和稳定运行。
2.2.2　各组双元素翼帆攻角或襟翼偏转角的调整方案
以Case 2方案为基础，在相对风向角为90°时，对各组双元素翼帆的攻角或襟翼偏转角进行调整（调整方案如表5所示），流线分布如图13所示，其中Structure A的三组双元素翼帆的襟翼吸力面仍发生了较大范围的流动分离，这主要是由于受襟翼偏转角过大引起翼帆失速所致；当襟翼偏转角减小到21°后，Structure B的Wingsail02和Wingsail03的襟翼流动分离很小，只有Wingsail01的襟翼仍存在一定程度的流动分离；当襟翼偏转角减小到19°而来流攻角增大至12°时，Structure C的翼帆流动未见分离，此时的助推力系数为2.171（见表6），较图11中Case 2方案提高了17.35%，而侧推力系数平均值仅为0.067；当来流攻角继续增大至14°时，Structure D的Wingsail01的吸力面出现了大尺度的流动分离，这容易引起翼帆失速。因此，选用Structure C方案的攻角和襟翼偏转角作为相对风向角为90°时双元素翼帆的调整方案是合适的。
2.3　相对风向角为120°时的干涉特性
2.3.1　不同间距的影响
为了分析相对风向角为120°时多组双元素翼帆相邻排列时的干涉特性，图14列出了相对风向角为120°时各组双元素翼帆的性能对比。可以看出，Case 2的助推力系数最大，而侧推力系数平均值仅有0.832，方向指向船舶左舷。此时，其翼帆流动尚未分离（如图15所示），满足设计要求，这与相对风向角为30°、90°时不同间距方案的择优结果一致，但Case 2的助推力系数并非最优，可通过改变攻角进一步提升双元素翼帆的推力性能。
2.3.2　各组双元素翼帆攻角的调整方案
为了提高相对风向角为120°时的助推力系数，在保证侧推力系数小于1.1以及翼帆不失速的前提下，可适当增大来流攻角。因此，以Case 2方案为基础，各组翼帆的攻角优化方案如表7所示，其流线分布如图16所示，可见，当三组双元素翼帆的来流攻角都增大至12°时Structure C的Wingsail03的吸力面出现大尺度流动分离，而Structure B的翼帆流动则未分离，且其助推力系数最大，为1.668，如表8所示，较图15中Case 2方案提高了5.2%，而侧推力系数平均值为0.869，方向指向船舶左舷。因此，选用Structure B方案的攻角设置作为相对风向角为120°时双元素翼帆的调整方案是合适的。
3　结语
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针对多帆干涉引起的双元素翼帆失速问题，本文提出了一种优化双元素翼帆的攻角和襟翼偏转角的方案，并研究双元素翼帆翼型的级间干涉特性。数值计算结果表明，在相对风向角为30°、90°和120°时，双元素翼帆的最佳横向间距为1.5c。然而，在相对风向角为90°和120°时，级间干涉会导致翼帆失速。经攻角和襟翼偏转角优化后，相对风向角为90°时双元素翼帆的整体助推力系数可提升17.35%以上，而相对风向角为120°时的整体助推力系数可提升5.2%以上，同时下游翼帆的流动分离现象消失。
基金
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  • 江苏海事职业技术学院科创基金资助项目(2022kjcx-01)
  • 江苏省“青蓝工程”优秀青年骨干教师资助项目
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2025年第29卷第7期
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doi: 10.3969/j.issn.1007-7294.2025.07.007
  • 接收时间：2025-01-19
  • 首发时间：2026-03-24
  • 出版时间：2025-07-20
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  • 收稿日期：2025-01-19
基金
江苏海事职业技术学院科创基金资助项目(2022kjcx-01)
江苏省“青蓝工程”优秀青年骨干教师资助项目
作者信息
    1.江苏海事职业技术学院机　电学院，南京　211170
    2.大连海事大学　轮机工程学院，辽宁　大连　116026
    3.江苏船舶节能减排工程技术研究开发中心，南京　211170
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