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Article(id=1213131708841509326, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1213131702797517129, articleNumber=null, orderNo=null, doi=10.19666/j.rlfd.202307112, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1689523200000, receivedDateStr=2023-07-17, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1767162738284, onlineDateStr=2025-12-31, pubDate=1708790400000, pubDateStr=2024-02-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1767162738284, onlineIssueDateStr=2025-12-31, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1767162738284, creator=13701087609, updateTime=1767162738284, updator=13701087609, issue=Issue{id=1213131702797517129, tenantId=1146029695717560320, journalId=1210938733613449225, year='2024', volume='53', issue='2', pageStart='1', pageEnd='198', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1767162736844, creator=13701087609, updateTime=1767168616029, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1213156361978954089, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1213131702797517129, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1213156361978954090, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1213131702797517129, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=86, endPage=92, ext={EN=ArticleExt(id=1213131709357408736, articleId=1213131708841509326, tenantId=1146029695717560320, journalId=1210938733613449225, language=EN, title=Parametric modeling and optimization of NACA63418 airfoil, columnId=1211002405299294959, journalTitle=Thermal Power Generation, columnName=Thermal energy science research, runingTitle=null, highlight=null, articleAbstract=

In wind turbines, the aerodynamic efficiency of wind turbines is closely related to the aerodynamic performance of excellent airfoils. Taking the conventional airfoil of wind turbine as the research object, combined with airfoil parametric modeling and self-adaptive genetic algorithm, the high performance optimized airfoil is obtained. The fitting accuracy of the conventional NACA63418 airfoil is compared between the CST method and the improved Hicks-Henne type function method, and then the Hicks-Henne type function method is selected to model the NACA63418 airfoil. The automatic calculation of aerodynamic characteristics of airfoil is realized by the coupling of self-adaptive genetic algorithm and XFOIL software, and the design efficiency of airfoil is improved. It broadens the train of thought and improves the design efficiency for the theoretical design of airfoils.

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风力发电机的风轮气动效率与优良翼型的气动性能密切相关。以风力机传统翼型为研究对象，结合翼型参数化建模及自适应遗传算法，寻优搜索得到高性能优化翼型。比较了CST法和改进的Hicks-Henne型函数法对于NACA63418传统翼型的拟合精度，进而选用Hicks-Henne型函数法对NACA63418翼型进行参数化建模。通过自适应遗传算法和XFOIL软件耦合实现翼型气动特性的自动计算，提高翼形的设计效率，为翼型的理论设计拓宽了思路。

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王丙申（1992），男，硕士研究生，主要研究方向为可再生能源利用技术和先进施工装备及技术，。
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张照煌（1963），男，博士，教授，主要研究方向为先进施工装备及技术和可再生能源利用技术，。

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张照煌（1963），男，博士，教授，主要研究方向为先进施工装备及技术和可再生能源利用技术，。

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张照煌（1963），男，博士，教授，主要研究方向为先进施工装备及技术和可再生能源利用技术，。

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China Mechanical Engineering, 2009, 20(2): 211-213., articleTitle=Integration study on airfoil profile for wind turbines, refAbstract=null)], funds=[Fund(id=1213131718693929902, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1213131708841509326, awardId=2019QN021, language=EN, fundingSource=Special Funds for Basic Scientific Research in Central Colleges and Universities(2019QN021), fundOrder=null, country=null), Fund(id=1213131718916228035, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1213131708841509326, awardId=2019QN021, language=CN, fundingSource=中央高校基本科研业务费专项资金资助(2019QN021), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1213131713170031208, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1213131708841509326, xref=null, ext=[AuthorCompanyExt(id=1213131713191002730, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1213131708841509326, companyId=1213131713170031208, 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articleId=1213131708841509326, language=CN, label=图6, caption=NACA63418翼型升阻性能对比, figureFileSmall=oV+VSeWYbXtMV3JIDV+FZw==, figureFileBig=eKjCLySGN2Uc1tze0O60Rg==, tableContent=null), ArticleFig(id=1213131718131893127, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1213131708841509326, language=EN, label=Tab.1, caption=

Geometric characteristics of NACA63418 airfoils

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翼型最大厚度/%最大厚度位置最大弯度/%最大弯度位置
NACA6341818.000.3432.210.513
优化翼型17.660.3572.770.538
), ArticleFig(id=1213131718232556432, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1213131708841509326, language=CN, label=表1, caption=

NACA63418翼型几何特性

, figureFileSmall=null, figureFileBig=null, tableContent=
翼型最大厚度/%最大厚度位置最大弯度/%最大弯度位置
NACA6341818.000.3432.210.513
优化翼型17.660.3572.770.538
), ArticleFig(id=1213131718333219736, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1213131708841509326, language=EN, label=Tab.2, caption=

Aerodynamic performance comparison of NACA63418 airfoils

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翼型升力系数阻力系数升阻比
NACA634180.931 10.006 4146.399
优化翼型1.033 60.006 5159.015
变化率/%11.001.568.62
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NACA63418翼型气动性能对比

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翼型升力系数阻力系数升阻比
NACA634180.931 10.006 4146.399
优化翼型1.033 60.006 5159.015
变化率/%11.001.568.62
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风电NACA63418翼型参数化建模及优化
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张照煌 , 王丙申 , 贾晓娜
热力发电 | 热能科学研究 2024,53(2): 86-92
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热力发电 | 热能科学研究 2024, 53(2): 86-92
风电NACA63418翼型参数化建模及优化
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张照煌 , 王丙申 , 贾晓娜
作者信息
  • 华北电力大学能源动力与工程学院，北京　102206

    • 张照煌（1963），男，博士，教授，主要研究方向为先进施工装备及技术和可再生能源利用技术，。

通讯作者:

王丙申（1992），男，硕士研究生，主要研究方向为可再生能源利用技术和先进施工装备及技术，。
Parametric modeling and optimization of NACA63418 airfoil
Zhaohuang ZHANG , Bingshen WANG , Xiaona JIA
Affiliations
  • School of Energy Power and Engineering, North China Electric Power University, Beijing 102206, China
出版时间: 2024-02-25 doi: 10.19666/j.rlfd.202307112
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摘要
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风力发电机的风轮气动效率与优良翼型的气动性能密切相关。以风力机传统翼型为研究对象，结合翼型参数化建模及自适应遗传算法，寻优搜索得到高性能优化翼型。比较了CST法和改进的Hicks-Henne型函数法对于NACA63418传统翼型的拟合精度，进而选用Hicks-Henne型函数法对NACA63418翼型进行参数化建模。通过自适应遗传算法和XFOIL软件耦合实现翼型气动特性的自动计算，提高翼形的设计效率，为翼型的理论设计拓宽了思路。

翼型  /  气动性能  /  参数化建模  /  自适应遗传算法

In wind turbines, the aerodynamic efficiency of wind turbines is closely related to the aerodynamic performance of excellent airfoils. Taking the conventional airfoil of wind turbine as the research object, combined with airfoil parametric modeling and self-adaptive genetic algorithm, the high performance optimized airfoil is obtained. The fitting accuracy of the conventional NACA63418 airfoil is compared between the CST method and the improved Hicks-Henne type function method, and then the Hicks-Henne type function method is selected to model the NACA63418 airfoil. The automatic calculation of aerodynamic characteristics of airfoil is realized by the coupling of self-adaptive genetic algorithm and XFOIL software, and the design efficiency of airfoil is improved. It broadens the train of thought and improves the design efficiency for the theoretical design of airfoils.

airfoil profile  /  aerodynamic performance  /  parametric modelling  /  self-adaptive genetic algorithm
张照煌, 王丙申, 贾晓娜. 风电NACA63418翼型参数化建模及优化. 热力发电, 2024 , 53 (2) : 86 -92 . DOI: 10.19666/j.rlfd.202307112
Zhaohuang ZHANG, Bingshen WANG, Xiaona JIA. Parametric modeling and optimization of NACA63418 airfoil[J]. Thermal Power Generation, 2024 , 53 (2) : 86 -92 . DOI: 10.19666/j.rlfd.202307112
正文
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以风力发电和光伏发电为主的可再生能源已经成为我国发展新能源的必然趋势[1]。风力机叶片是由展向不同位置的翼型堆叠而成，传统的水平轴风力机常用翼型家族包括NACA 44XX、NACA 23XXX、NACA 63XXX和NASA LS系列翼型[2]。针对翼型的研究，上世纪80年代后美国、丹麦等国家先后开展了风力机先进翼型的研究，比较著名的有美国NERL-S系列[3]、丹麦RISØ系列[4]、荷兰DU系列[5]、瑞典FFA-W系列[6]等。国产风力机翼型族有西北工业大学乔志德等[7]设计的NPU-WA翼型族，以及中科院工程热物理所白井艳等[8]开发的CAS系列。其中，CAS系列采用正向设计方法需要搜集大量的翼型数据，不断反复拟合优化，但仍会遗漏很多优化方案[9]；NPU-WA翼型系列采用反向设计方法。随着优化算法的迅速发展，正向设计法成为主流[10]。
一般来说，叶片翼型设计主要有翼型气动性能计算和翼型设计优化2部分。现代设计中常用计算流体力学（CFD-FLUENT）或XFOIL软件对风力机翼型进行气动性能计算。CFD-FLUENT计算模型将研究对象划分为计算网格，对每个网格都进行N-S方程离散化求解，计算时间巨大[11]。基于面元法的XFOIL软件能较准确地进行翼型气动计算，也发展得比较成熟，得到了工程应用的认可，且计算速度较快，特别适用于快速迭代和参数化研究，可大幅缩短翼型开发周期[12]。
本文采用正向设计法，在NACA翼型的基础上，使用改进的Hicks-Henne型函数法进行参数化建模[13-14]，再通过自适应遗传算法调用XFOIL软件搜索找到高性能的优化翼型，尝试探索用时较少、效率较高的翼型设计路径，为翼型设计拓宽思路，提供借鉴。
1　翼型优化
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叶片的主要功率产生区位于75%展长附近翼型[15]，因此，本文采用叶尖位置气动性能要求较高的NACA63418作为基础翼型。将翼型气动计算软件和数值优化算法结合起来，通过改变翼型几何描述参数找到气动特性最佳的翼型几何形状。首先，分别采用CST法[16]和改进的Hicks-Henne型函数法对翼型参数化建模，并比较这2种方法的表达精度。然后，利用对风力机翼型的计算较为准确和用时较少的XFOIL软件[17-18]作为气动特性求解器；最后结合自适应遗传算法，以翼型特定攻角下的最大升阻比为优化目标来找到设计翼型。
1.1　翼型参数化建模及精度对比
为保证翼型外形足够光滑连续，翼型设计前期需要对翼型参数化建模。现有多种表征翼型几何形状的参数化方法，这些方法各有特点，适用不同场合。以传统翼型NACA63418为例，选择CST方法和改进的Hicks-Henne型函数分别对翼型参数化建模，分析不同阶数下的拟合精度，找到适用设计翼型的建模方法。
翼型的参数化通常采用尽可能少的设计变量来达到较好控制翼型形状的效果。通过CST法和改进的Hicks-Henne型函数法对NACA63418翼型进行最小二乘拟合，并对比其表述精度。采用上下翼型线纵坐标的残差[19]来描述2种参数化方法的拟合精度。
e=yi−y0i
式中：e为拟合残差：yi和y0i分别为拟合翼型和基准翼型的纵坐标。
通过最小二乘求得不同阶数下的拟合精度，结果如图1、图2所示。
由图1和图2看出：CST法和改进的Hicks-Henne型函数法都能对预估翼型实现较精确拟合；随着变量维数的增加，2种参数化方法的拟合残差呈减小趋势，尤其从6维增至8维变量，改进Hicks-Henne型函数法拟合精度明显提高。CST方法对不同类别的翼型控制能力存在较大差别，使用MATLAB软件[20]翼型拟合过程中，需选用合适的初始化参数，参数设置不当，极易产生不光顺翼型或尾缘交叉翼型。改进的Hicks-Henne型函数法无需考虑初始参数的影响，可在基准翼型的基础上对设计翼型进行调整，8维变量表征翼型时精度较高。
1.2　采用XFOIL软件计算翼型特性
翼型气动性能数据主要通过风洞实验、理论分析及数值计算等途径来获取。风洞实验获取的数据准确，但数据非常有限且实验成本昂贵。XFOIL软件能有效避免该问题[8]，将设计翼型NACA63418的气动性能与风洞实验数据对比分析[21]，结果如图3所示。
由图3可见，在雷诺数Re=3×106，自由转捩的工况下，攻角范围为0°~10°，XFOIL软件计算的升阻力系数与实验数据非常接近，且变化趋势相同，但同样大攻角失速状态下的数据有较大偏差。这也侧面说明XFOIL软件预测大攻角翼型流动不准确的特点。虽然数值计算的方法不能完全准确预测翼型的气动特性，但目前风力机翼型正常运行的攻角在小攻角范围内，故通过XFOIL软件计算也具有参考性。
2　自适应遗传算法翼型气动优化模型
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结合上节相关内容，选用改进的Hicks-Henne型函数法8维变量表征翼型具有较高精度，可通过此方法参与后续设计。针对叶片不同展向位置翼型的运行特点及设计要求，通过自适应遗传算法耦合XFOIL软件来实现翼型气动性能的自动计算，进而完成翼型的气动优化设计。
2.1　自适应遗传算法
遗传算法（GA）是依据遗传学机理演化而来的随机全局寻优算法[22]，通常能较快速找到最佳结果。为提高算法的收敛能力[23]，本文采用Srinvivas提出的自适应遗传算法，使交叉概率Pc及变异概率Pm能随适应函数值自由变化[24]，自适应参数Pc及Pm的表达式分别为：
Pc={0.9−0.300(f'−favg)fmax−favg     f'≥favg0.9                                  f'<favg
Pm={0.1−0.099(fmax−f)fmax−favg     f≥favg0.1                                  f<favg
式中：f′为交叉个体中较大的适应值；f avg为种群平均适应值；f max为群体中最大适应值；f为变异个体的适应值；0.300为交叉率的变化值；0.099为变异率的变化值。
这种自适应遗传算法虽然收敛速度较慢但能够维持群体多样性。本文建立的风力机翼型气动优化模型则基于自适应遗传算法（adaptive genetic algorithm）的变量算子复制、交叉及变异实现，并通过算法与气动分析软件XFOIL耦合对翼型进行单目标优化设计。
2.2　优化设计模型
采用基函数系数为设计变量[25]，通过调整控制变量条件和翼型形状约束，结合自适应遗传算法和XFOIL气动求解器找到气动特性更佳的优化翼型。图4为翼型优化设计流程，优化算法多次迭代调用XFOIL软件评估翼型特性，待达到优化终止条件，算法停止并返回优化翼型。
1）目标函数选取
NACA63418翼型风力机叶片位于叶尖位置，该翼型要求较高的风能捕捉能力，偏高的最大升阻比及和缓的失速能力[26]。因此，本文以风力机翼型的升阻比及升力系数最大为多目标优化函数。采用权重系数法，优化变量的权重系数为0.5。由于升力系数与升阻比数值上差异近2个数量级，故取0.01倍的升阻比和升力系数为优化目标，将多目标优化求解转化为单目标求解问题。目标函数表示为：
f(x)=0.5×0.01max(Cl/Cd)+0.5max(Cl)
式中：Cl和Cd分别为升力系数和阻力系数。
2）设计变量的选取
采用改进的Hicks-Henne型函数法的基函数系数为设计变量[27]。通常参数化建模过程中设计变量数目增多，表征能力较强，但控制变量数目太多会大幅增长优化时间。因此，选择上下翼型面各8个设计变量：
c=[c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,       c11,c12,c13,c14,c15,c16]
式中：c1—c8为上翼型面控制变量；c9—c16为下翼型面的控制变量。
3）优化约束条件
翼型的最大厚度及其弦长相对位置等几何参数对气动特性能产生较大影响，需对翼型形状参数进行相应约束。为避免改进Hicks-Henne型函数法建立的扰动函数出现不具备控制翼型形状的特征，控制变量的范围为–0.005<ci<0.005。
4）优化算法的实现
本文采用MATLAB软件编写翼型优化程序，在设计变量空间内随机生成初始种群，XFOIL软件作为翼型气动求解器，AGA自适应算法种群规模取20，迭代次数取100，变量采用二进制编码。
2.3　优化实例
基准翼型：NACA63418翼型，使用改进的Hicks-Henne型函数法，攻角为5°，雷诺数Re= 3×106。目标函数：远方来流速度为6 m/s，翼型的升阻比及升力系数最大，即目标函数f(x)。设计变量：基函数系数ci为设计变量，上下翼型线各选8个扰动点，共16个变量。约束条件：设计变量控制在[–0.005,0.005]范围内，翼型形状约束包括翼型的最大厚度控制在17.50%~18.50%，最大厚度位置控制在25.00%~40.00%。经自适应遗传算法优化，找到优化翼型如图5所示。
在给定设计变量的边界空间搜索最优翼型，程序停止搜索到相较于基准翼型气动参数更优的翼型，其设计变量取值和优化前后的几何特性见表1。由表1可见：翼型厚度有所减小，由初始18.00%减小到17.66%，最大厚度位置向后缘移动；相应地，翼型弯度增大，最大弯度位置也向后缘移动。
算法耦合XFOIL软件计算得到基准翼型和优化翼型在设计攻角下的气动参数见表2。由表2可见，翼型的升力系数增长11.00%，升阻比增长8.62%，能达到翼型优化的效果。
图6为优化翼型与初始翼型的升阻性能比较。
由图6可见，相较基础NACA63418翼型，优化翼型多攻角范围内的升力都明显增大，阻力变化较小，升阻比也呈增大趋势。
通过CST法和改进的Hicks-Henne型函数法描述设计翼型，确定改进Hicks-Henne型函数法能精确描述翼型轮廓，且设计空间充足，但参数不宜过多。翼型优化过程涉及频繁调用XFOIL，通过算法调用XFOIL软件可实现MATLAB环境下翼型性能的自动分析计算，着重考虑翼型的升阻比及升力系数气动特性，量化分析表明优化后翼型的性能所提升。
3　结论
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1）为提升风力机翼型叶片性能，本文对翼型进行了气动优化设计。变量维数的增加能提高CST法和改进Hicks-Henne型函数法2种参数化方法的表征精度，但维数过大会影响计算成本时间。相较于CST，改进Hicks-Henne型函数法无需设定初始参数，且表征稳定不易出现波浪翼型，确定8阶变量下的基函数系数为设计变量。
2）以NACA63418翼型的基函数系数为设计变量进行寻优设计，优化翼型的升力系数增长11.00%，升阻比增长8.62%.
3）实例仿真证明，在正向设计方法路径中，采用MATLAB和XFOIL软件数值计算结合，可有效提高了设计效率。
基金
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  • 中央高校基本科研业务费专项资金资助(2019QN021)
文献
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2024年第53卷第2期
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doi: 10.19666/j.rlfd.202307112
  • 接收时间：2023-07-17
  • 首发时间：2025-12-31
  • 出版时间：2024-02-25
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  • 收稿日期：2023-07-17
基金
Special Funds for Basic Scientific Research in Central Colleges and Universities(2019QN021)
中央高校基本科研业务费专项资金资助(2019QN021)
作者信息
    华北电力大学能源动力与工程学院，北京　102206

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王丙申（1992），男，硕士研究生，主要研究方向为可再生能源利用技术和先进施工装备及技术，。
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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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