向锦武,张雪娇,赵仕伟,程云,张志飞,李道春
(北京航空航天大学 航空科学与工程学院,北京 100191)
摘要:
长航时无人机普遍采用轻质、高比强度复合材料结构大展弦比机翼,该类机翼在飞行过程中表现出显著的几何非线性和气动非线性,进而导致机翼的气动弹性非线性.大展弦比复合材料机翼的设计分析方法与传统机翼有很大不同.为研究大展弦比复合材料机翼的进展,并预测其未来可能的发展方向,对现有大展弦比复合材料机翼设计、分析、试验方法进行分析总结.首先,对大展弦比复合材料机翼结构设计方法、结构分析方法进行了介绍;然后,介绍了两类用于大展弦比机翼的气动力分析方法:基于片条理论和二元非定常气动力相结合的气动力分析方法以及考虑展向流动效应的三维气动力分析方法,重点总结了复合材料大展弦比机翼静气动弹性、动气动弹性分析方法以及主动控制技术在大展弦比机翼中的应用,并分析了大展弦比复合材料机翼气动弹性剪裁最新进展;最后,综述了大展弦比复合材料机翼试验研究进展.基于文献分析可知,现有大展弦比复合材料机翼的结构模型多采用等效梁板模型,气动模型多采用片条理论与考虑动失速的二元非定常气动力相结合的模型.气动降阶模型与结构模型相耦合进行相关研究,以及大展弦比复合材料机翼的飞行试验,均是大展弦比复合材料机翼未来可能的研究发展方向.
关键词: 大展弦比 几何非线性 气动非线性 气动弹性 主动控制
DOI:10.11918/j.issn.0367-6234.201705036
分类号:V271.4
文献标识码:A
基金项目:国家自然科学基金(4,3)
Recent advance in high-aspect-ratio composite wing
XIANG Jinwu,ZHANG Xuejiao,ZHAO Shiwei,CHENG Yun,ZHANG Zhifei,LI Daochun
(School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China)
Abstract:
The high-aspect-ratio composite wing is generally used in long-endurance Unmanned Aerial Vehicle (UAV), which uses lightweight and high-specific-strength composite structure. This type of wing has significant geometric nonlinearity and aerodynamic nonlinearity during the flight, which further leads to the aeroelastic nonlinearity of the wing. There is a huge difference for design analysis method between the high-aspect-ratio composite wing and the conventional wing. In order to summarize the research status and forecast the future research direction of the high-aspect-ratio composite wing, this paper analyzes and summarizes the design, analysis and experiment methods of the existing high-aspect-ratio composite wing. The aeroelastic characteristics of wing would be affected by the geometric and aerodynamic nonlinearities. The structural design and structural analysis methods of high-aspect-ratio composite wing are introduced. Two kinds of aerodynamic analysis methods are introduced: the aerodynamic analysis method based on the strip theory and binary unsteady aerodynamic method and three dimensional aerodynamic analysis method considering spanwise flow effect. Static aeroelasticity method, dynamic aeroelastic analysis method and active control technology applied in the high-aspect-ratio wing are introduced. The recent advance in aeroelastic tailoring of high-aspect-ratio composite wing is analyzed. Finally, the experimental research progress of high-aspect-ratio composite wing is introduced. Based on the literature analysis, it can be seen that the structural model of the existing high-aspect-ratio composite wing adopts the equivalent beam plate model, while the aerodynamic model adopts the combination of the strip theory and the binary unsteady aerodynamics considering the dynamic stall. The flight test, as well as the research based on the coupling of aerodynamic reduced-order model and the structural model of the high-aspect-ratio composite wing may be the research and development directions of the high-aspect-ratio composite wing in the future.
Key words: high-aspect-ratio geometric nonlinearity aerodynamic nonlinearity aeroelastic active control
向锦武, 张雪娇, 赵仕伟, 程云, 张志飞, 李道春. 大展弦比复合材料机翼研究进展[J]. 哈尔滨工业大学学报, 2017, 49(10): 1-14. DOI: 10.11918/j.issn.0367-6234.201705036.
![复制到剪切板](http://hit.alljournals.cn/html/hitxb_cn/2017/10/images/copy.gif)
XIANG Jinwu, ZHANG Xuejiao, ZHAO Shiwei, CHENG Yun, ZHANG Zhifei, LI Daochun. Recent advance in high-aspect-ratio composite wing[J]. Journal of Harbin Institute of Technology, 2017, 49(10): 1-14. DOI: 10.11918/j.issn.0367-6234.201705036.
![复制到剪切板](http://hit.alljournals.cn/html/hitxb_cn/2017/10/images/copy.gif)
基金项目 国家自然科学基金(11402014,11572023) 作者简介 向锦武(1964—), 男, 博士生导师, “****”特聘教授 通信作者 李道春, lidc@buaa.edu.cn 文章历史 收稿日期: 2017-05-07
Contents -->Abstract Full text Figures/Tables PDF
大展弦比复合材料机翼研究进展
向锦武, 张雪娇, 赵仕伟, 程云, 张志飞, 李道春
![通讯作者](http://hit.alljournals.cn/html/hitxb_cn/2017/10/images/REcor.gif)
![lidc@buaa.edu.cn](http://hit.alljournals.cn/html/hitxb_cn/2017/10/images/REemail.gif)
北京航空航天大学 航空科学与工程学院,北京 100191
收稿日期: 2017-05-07
基金项目: 国家自然科学基金(11402014,11572023)
作者简介: 向锦武(1964—), 男, 博士生导师, “****”特聘教授
通信作者: 李道春, lidc@buaa.edu.cn
摘要: 长航时无人机普遍采用轻质、高比强度复合材料结构大展弦比机翼,该类机翼在飞行过程中表现出显著的几何非线性和气动非线性,进而导致机翼的气动弹性非线性.大展弦比复合材料机翼的设计分析方法与传统机翼有很大不同.为研究大展弦比复合材料机翼的进展,并预测其未来可能的发展方向,对现有大展弦比复合材料机翼设计、分析、试验方法进行分析总结.首先,对大展弦比复合材料机翼结构设计方法、结构分析方法进行了介绍;然后,介绍了两类用于大展弦比机翼的气动力分析方法:基于片条理论和二元非定常气动力相结合的气动力分析方法以及考虑展向流动效应的三维气动力分析方法,重点总结了复合材料大展弦比机翼静气动弹性、动气动弹性分析方法以及主动控制技术在大展弦比机翼中的应用,并分析了大展弦比复合材料机翼气动弹性剪裁最新进展;最后,综述了大展弦比复合材料机翼试验研究进展.基于文献分析可知,现有大展弦比复合材料机翼的结构模型多采用等效梁板模型,气动模型多采用片条理论与考虑动失速的二元非定常气动力相结合的模型.气动降阶模型与结构模型相耦合进行相关研究,以及大展弦比复合材料机翼的飞行试验,均是大展弦比复合材料机翼未来可能的研究发展方向.
关键词: 大展弦比 几何非线性 气动非线性 气动弹性 主动控制
Recent advance in high-aspect-ratio composite wing
XIANG Jinwu, ZHANG Xuejiao, ZHAO Shiwei, CHENG Yun, ZHANG Zhifei, LI Daochun
![Corresponding author](http://hit.alljournals.cn/html/hitxb_cn/2017/10/images/REcor.gif)
![lidc@buaa.edu.cn](http://hit.alljournals.cn/html/hitxb_cn/2017/10/images/REemail.gif)
School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China
Abstract: The high-aspect-ratio composite wing is generally used in long-endurance Unmanned Aerial Vehicle (UAV), which uses lightweight and high-specific-strength composite structure. This type of wing has significant geometric nonlinearity and aerodynamic nonlinearity during the flight, which further leads to the aeroelastic nonlinearity of the wing. There is a huge difference for design analysis method between the high-aspect-ratio composite wing and the conventional wing. In order to summarize the research status and forecast the future research direction of the high-aspect-ratio composite wing, this paper analyzes and summarizes the design, analysis and experiment methods of the existing high-aspect-ratio composite wing. The aeroelastic characteristics of wing would be affected by the geometric and aerodynamic nonlinearities. The structural design and structural analysis methods of high-aspect-ratio composite wing are introduced. Two kinds of aerodynamic analysis methods are introduced: the aerodynamic analysis method based on the strip theory and binary unsteady aerodynamic method and three dimensional aerodynamic analysis method considering spanwise flow effect. Static aeroelasticity method, dynamic aeroelastic analysis method and active control technology applied in the high-aspect-ratio wing are introduced. The recent advance in aeroelastic tailoring of high-aspect-ratio composite wing is analyzed. Finally, the experimental research progress of high-aspect-ratio composite wing is introduced. Based on the literature analysis, it can be seen that the structural model of the existing high-aspect-ratio composite wing adopts the equivalent beam plate model, while the aerodynamic model adopts the combination of the strip theory and the binary unsteady aerodynamics considering the dynamic stall. The flight test, as well as the research based on the coupling of aerodynamic reduced-order model and the structural model of the high-aspect-ratio composite wing may be the research and development directions of the high-aspect-ratio composite wing in the future.
Key words: high-aspect-ratio geometric nonlinearity aerodynamic nonlinearity aeroelastic active control
长航时无人机能够不间断地执行情报/侦察/监视、目标捕捉、国土边防监控、气象科学研究、通信中继和环境监测等许多重要军用/民用任务,而且比卫星更可控,成本更低、方式更灵活,且更易维护,因此该类飞行器成为航空研究的热门领域.其中具有代表性的太阳能无人机是美国航空环境(AeroVironment)公司的“太阳神”(Helios)系列无人机[1]、美国波音公司的“太阳鹰”(SolarEagle)无人机、英国奎奈蒂克(QinetiQ)公司的“西风”系列无人机[2]、意大利都灵工业大学的“太阳能平台”(HELIPLAT)无人机[3].代表性长航时氢动力无人机有航空环境公司的“全球观察者”系列无人机[4]、极光飞行科技公司(Aurora Flight Sciences)的“猎户座”(Orion HALL)无人机和波音公司的“鬼眼”(Phantom Eye)无人机[5]等.
长航时无人机为获得高升阻比,普遍采用轻质复合材料和大展弦比设计.结构大柔性引起几何非线性,导致气动载荷重新分布,从而改变结构的气动弹性特性.高空低速飞行时,局部攻角较大,且受结构大变形的影响,容易发生气动失速,出现流动分离,从而表现出气动非线性.结构非线性和气动非线性耦合,将引起新的非线性气动弹性特性.基于上述分析可以看出,大展弦比复合材料机翼的设计分析方法和传统机翼不同,有必要对现有大展弦比复合材料机翼的设计、分析、试验方法进行分析总结.本文对大展弦比复合材料机翼结构、气动、气弹、主动控制、气弹剪裁、试验方法进行综述,最后对研究现状进行总结,并提出了可能的研究方向.
1 大展弦比复合材料机翼结构设计分析方法大展弦比机翼由于气动力的作用,翼根承受较大的弯矩,而复合材料比强度高,比模量大,刚度可设计,因此复合材料被广泛应用于大展弦比机翼结构.由于结构柔性导致的结构几何非线性的影响,如图 1所示.大展弦比复合材料机翼的分析和设计方法与传统机翼不同,本部分介绍大展弦比复合材料机翼结构的设计和分析方法.
Figure 1
![点击查看原图](http://hit.alljournals.cn/html/hitxb_cn/2017/10/PIC/hebgydxxb-49-10-1-1.jpg)
1.1 大展弦比复合材料机翼结构设计方法大展弦比机翼的特点是翼根处弯矩较大,上翼面易发生屈曲,以及机翼的扭转变形可能过大等.针对上述特点,合理应用复合材料可以显著提升结构的性能.首先,复合材料可以增大机翼的刚度特性,田坤黉等[6]通过有限元分析计算,可知在展弦比不变的条件下,复合材料机翼结构的各阶固有频率明显高于全铝合金机翼结构.复合材料各向异性的特点还有助于机翼的减重.刘峰等[7]对某无人机复合材料主翼盒运用等强度设计的思想研究了主翼盒基于载荷分段的包络设计方法与铺层优化方法.给出了翼盒前、后梁的上下表面的初步铺层设计,可使结构减重达5.23%.Benjamin等[8]将复合材料机翼进行分块制造拼装,具有轻量化、检修方便的特点,可实现整个机翼的主动扭转弯曲.国内外学者对机翼结构所用的复合材料的铺设角大小和铺层厚度进行了研究.Myoungkeon等[9]指出复合材料结构,采用较多的±45°铺层,并且铺层位于外侧时,结构的屈曲强度和弯曲强度较好.杨龙[10]分析了机翼主梁碳纤维铺层厚度与机翼结构动力学特性的关系,发现综合刚度和厚度考虑,碳纤维铺层并不是越厚性能就越好,而是存在某个最佳值.
在风洞试验和飞行试验中常常用到缩比模型,大展弦比机翼缩比模型设计除了考虑常规的相似准则以外,还要考虑非线性对相似律的影响.French等[11]在布金汉π定理的基础上,提出两步法建立缩比模型,先使设计模型与目标模型之间的差异尽可能的小,然后在保证刚度等效的条件下,对模型进行降阶处理.Richards等[12]评估了联合翼飞行测试程序的两种线性缩比方法.第1种方法使用单步直接模态匹配,将固有频率和对应的模态形状同时分析, 设计变量包括结构刚度和非结构的质量.第2种方法先对刚度和非结构质量解耦,然后采用文献[11]的方法进行设计.两种方法结果比较一致,但是第1种的计算量较大.Wan[13]指出线性相似准则对几何非线性的结构仍然适用.但是模型之间除了需要满足几何相似、质量相似、气动弹性相似外,弗劳德数相似也不可忽略,同时还应满足刚度相似,[KT]=[KL]+[KNL]+[Kσ].其中: KT为全局坐标系里一个单元的纵向刚度矩阵; KL为小变形线性刚度矩阵; KNL为大变形,非线性刚度矩阵;Kσ为预应力刚度矩阵.
综上所述,大展弦比复合材料机翼的设计难点在于如何分配刚度,使得机翼在满足所需动力学特性的基础上质量更轻.复合材料结构形式上可以选用蜂窝夹层、多墙式和混合式结构.随后,可以对复合材料的铺设角、厚度等进行进一步的设计.大展弦比机翼缩比模型的设计要考虑非线性对相似准则的影响,为后续的风洞试验奠定基础.
1.2 大展弦比复合材料机翼结构分析方法机翼结构一般可分为有限元和理论模型两种分析方法.其中有限元法发展的比较成熟,适用于详细设计阶段,计算较为精确.Zhe等[14]运用非线性方法,基于有限元模型,通过施加阵风分析了机翼结构的力学性能.石庆华等[15]在剪切梁理论的基础上,采用9节点平面单元模拟梁任意截面形状,可用于复杂结构空间薄壁复合材料梁的有限元分析计算.
而简化模型则适用于概念设计阶段的后期,实现快速分析.1974年,Hodges等[16]最早提出了旋翼桨叶的非线性梁模型, 该模型可用于具有中等位移的各向同性均匀预扭梁的分析.2003年,Hodges[17]又通过广义速度、广义应变与位移的关系,推导了本征运动学方程,建立了不含位移和有限转动变量,完全本征的几何精确各向异性运动梁模型.国内方面,谢长川等[18]应用“准模态”假设分析了几何非线性对结构振动的影响.随后张新榃等[19]通过实验验证了准模态法在颤振分析中的准确性.石庆华等[20]假设应变沿薄壁厚度呈二次曲线形式变化,基于Timoshenko梁模型,建立了一种新的考虑剪切、翘曲复合材料大变形梁静、动态特性分析模型,并进行了算例验证.Palacios等[21]结合二维截面分析方法与Hodges一维非线性梁模型,建立了嵌入传感器和压电驱动器的细长结构梁模型.王睿等[22]利用空间缩聚法提升了Hodges的本征梁模型的运算速度.
如果同时考虑弦向和展向两个方向的弯曲变形,可以将结构简化为板模型.传统的板弯曲理论是Kirchhof薄板理论,此理论能很好地满足力边界条件,但对中厚板或者一些面内弹性模量之比较大的复合材料层合板而言,横向剪切变形的影响不应忽略.沈惠申等[23]提出了一阶剪切变形理论.但该理论不能精确满足力边界条件,需要引入剪切因子作为修正,且修正过程相当繁琐.为了不引进剪切因子并满足板上、下表面的力边界条件,种种高阶剪切变形理论被提出.黄志强等[24]将Reddy的变形理论应用于复合材料层合板的面内应力分布,及各向同性方板的非线性弯曲计算,对复合材料机翼的结构分析也具有一定的参考价值.杨佑绪等[25]基于一阶剪切变形板理论开发了一种导弹翼面部件的动力学和颤振分析方法.
综上所述,大展弦比机翼大多采用等效梁模型,如果弦向变形不可忽略,可以采用文献[19]所述的变截面梁模型或采用剪切板模型,均可以得到较为准确的计算结果.
2 大展弦比复合材料机翼气动力分析方法高效准确的气动力分析方法是大展弦比机翼气动建模的关键.大展弦比机翼气动分析可以分为基于片条理论和二元非定常气动力相结合的气动力分析方法以及考虑展向流动效应的三维气动力分析方法.
2.1 二维气动力分析方法片条理论和二元非定常气动力相结合的气动模型,计算效率较高,被广泛应用于大展弦比机翼气动弹性分析[26],二元翼型非定常气动力模型主要包括频域分析模型和时域数值模型.
Theodorson非定常气动力模型能够较精确和高效地描述二元薄板在小攻角下非定常气动力的变化,被广泛应用于大展弦比机翼的气动弹性分析.然而,频域分析模型基于薄板简谐振动进行气动力计算,近似认为贴近颤振边界时有效,因此不适用于远离颤振边界的气动弹性响应分析.
二元翼型时域数值模型能够描述二元翼型在任意运动形式下的气动力变化,具有更广泛的适用性.文献[27]对动力入流理论的诞生和发展进行了总结.动力入流模型数学形式简洁,而且计算效率较高,适用于大展弦比柔性飞行器气动弹性分析[28-29].动失速模型针对的是二元翼型大攻角情况下的气动失速,通过二元翼型风洞试验数据对模型中的系数进行辨识和修正.其中应用较为广泛的半经验动失速模型主要包括Leishman-Beddoes (L-B)模型和ONERA模型等.文献[30]对L-B的发展进行了回顾.该模型主要包括静态模型、附着流模型、分离流模型和涡旋流模型4部分,能够较准确地计算二维翼型的气动升力、俯仰力矩和阻力,而且经验系数较少,但目前多用于旋翼桨叶气动弹性分析以及各种不同动失速模型准确性的对比和评价.ONERA动失速模型中包含了较多的经验参数,但其表达形式简洁,其易于与结构模型耦合,已被用于气动弹性分析[31-33].
2.2 三维气动力分析方法计算三维气动力的数值方法主要有偶极子网格法和非定常涡格法.偶极子网格法通常用于固定翼的气动弹性分析,由于大展弦比机翼变形较大,偶极子网格无法模拟大变形状态下的曲面.非定常涡格法通过在物面和尾迹区域布置涡格,涡格的形状可以随着物面的形状变化而变化.因此,通常采用非定常涡格法计算大展弦比机翼非定常气动力[34-37].传统的非定常涡格法是基于时间序列进行分析计算,然而由于控制律以及稳定性分析的需求,需要对非定常涡格法进行线性化.Murua等[34]对非定常涡格线性化进而计算配平状态的大展弦比机翼的稳定性.
此外,计算流体力学方法(CFD)也常被用于大展弦比机翼的气动弹性分析计算[38-39],目前多用于静气动弹性分析和动响应分析,计算效率较低.为提高计算效率,可采用基于CFD的降阶模型进行气动力建模.常用的降阶模型方法包括基于流场内部特征结构分析的本征正交分解方法(POD)以及基于系统辨识的方法,如Volterrra级数方法、ARMA方法等,相关研究工作详见文献[40-41].
3 大展弦比复合材料机翼气动弹性分析方法为有效减轻质量,大展弦比机翼多采用复合材料.复合材料的各向异性和几何非线性特性, 使机翼气动弹性问题更加复杂.国内外学者对复合材料机翼的气动弹性问题进行了较深入的研究.具体可分为静气动弹性、动气动弹性以及阵风减缓与主动控制.
3.1 静气动弹性Smith等[42]基于几何精确本征梁理论和Euler求解器,研究了大展弦比柔性机翼的静态气动弹性特性.Joseph等[43-44]耦合三维几何非线性梁模型与Euler/Navier-Stokes CFD方法,研究了大展弦比柔性机翼跨音速静气动弹性特性.其直机翼算例结果显示,非线性模型与线性模型的机翼扭转显著不同,主要归因于跨音速阻力与机翼弯曲大变形的耦合作用;后掠翼算例结果显示,机翼翼尖处易发生失速.
针对大展弦比复合材料机翼的静气动弹性特性分析, 国内学者[19, 32, 45-49]大多采用线性结构模型及气动模型, 没有考虑复合材料机翼的刚度耦合问题.在此基础上,Lu等[50]将一维非线性梁的结构模型与非定常涡格法气动模型相耦合,研究大展弦比柔性翼的静气动弹性特性.郝帅等[51]针对氢动力超长航时无人机大展弦比机翼,基于CFD/CSD强耦合,给出了一种考虑静气动弹性效应的刚性机翼气动特性修正方法.张强等[52]基于CFD/CSD松耦合,研究了大展弦比飞翼布局无人机的静气动弹性问题.
3.2 动气动弹性20世纪中期,非线性气动弹性的相关研究已经起步.李道春[53]以二元翼型为对象,较详细地研究了结构刚度非线性对二元翼型非线性气动弹性的影响,并进行了非线性颤振主动控制的研究.上述研究侧重于结构刚度非线性对飞行器气动弹性的影响,忽略了结构几何非线性的作用.针对大展弦比复合材料机翼,结构大变形引起的几何非线性也会改变结构的振型和频率,影响机翼的气动弹性特性.传统气动弹性分析方法都不考虑几何非线性的影响,在进行气动弹性分析预测时会产生较大误差,因此有必要针对大展弦比柔性机翼进行非线性气动弹性分析.
3.2.1 非线性颤振随着大展弦比柔性机翼非线性结构建模的深入研究,Tang等[54]开展了基于Hodges-Dowell非线性运动梁模型的大展弦比机翼气动弹性的理论和实验研究,其结果表明大展弦比柔性机翼的结构变形对弯曲和扭转特性影响较大,二元机翼无法精确模拟大展弦比柔性机翼的结构几何非线性效应,以及结构变形引起的弯曲与扭转刚度的非线性变化.Patil等[55-57]针对大展弦比HALE飞机的非线性气动弹性和飞行动力学及控制问题进行了较完整的研究,大展弦比机翼的结构动气动弹性特性会受到结构几何非线性和机翼变形状态的影响.基于几何精确本征梁,Cesnik等[58]针对大展弦比复合材料柔性机翼建立了低阶高精度的非线性气动弹性分析模型,研究了复合材料铺层角对线性发散和线性颤振的影响,分析了几何非线性对静气动弹性变形和发散临界动压的显著影响.
国内的赵永辉等[59-60]研究了大展弦比复合材料机翼的线性颤振,气动力模型采用ONERA-EDlin动失速模型,结构模型忽略了几何非线性,非线性时域响应求解是通过结构模型和气动模型间的数据独立传递来实现的.刘湘宁等[61-62]基于结构几何非线性的大变形欧拉梁和ONERA动失速模型,建立了大展弦比复合材料机翼的非线性气动弹性分析模型,对复合材料机翼的非线性失速颤振特性和剪裁刚度的影响进行了较为详尽的研究.张健等[63]基于本征梁理论研究了侧向随动载荷作用下柔性机翼的气动弹性稳定性,分析了机翼刚度比、集中质量大小和位置、机翼后掠角和上反角等参数对侧向随动载荷作用下柔性机翼稳定性的影响.
3.2.2 极限环振荡当来流速度高于颤振速度时,线性气动弹性系统受到小扰动后,其响应振幅会不断增大直至结构破坏.而在非线性气动弹性系统中,鉴于几何刚化效应和气动非线性特性,振幅在响应初期不断增大,最终进入振幅有限的振动状态,表现为极限环振荡现象.振幅不变的情况下,极限环振荡能有效避免气动发散引起的结构破坏,但会导致结构疲劳,降低结构寿命, 因此有必要研究极限环振荡.
Patil等[57, 64, 87]分别针对小展弦比和大展弦比柔性机翼的极限环振荡特性进行了研究,模型中考虑了结构几何非线性和气动失速非线性的作用.结果表明,当来流速度大于颤振速度,或来流速度小于颤振速度但扰动足够大时,机翼均会发生极限环振荡,并且随着速度的增加,极限环振荡频率成分增多,表现为多周期运动,速度继续增大时甚至出现混沌.Kim等[65]在Crespo非线性梁模型中加入了外挂,研究外挂非线性对机翼极限环振荡的影响.Kouchakzadeh等[66]和Kuo[67]将机翼简化成复合材料板, 研究了超音速颤振问题.Attaran等[68]建立复合材料板, 分析了后掠角、展弦比等对颤振速度的影响.Kameyama等[69]建立变截面的复合材料板, 并研究后掠角、纤维铺层角对颤振发散特性的影响.
国内有关几何非线性的大展弦比柔性机翼/飞机极限环振荡的研究也已开展,但仍较少.张健等[32]基于几何精确本征梁和Extended-ONERA动失速模型,对大展弦比机翼的极限环振荡现象进行了研究,结果表明气动阻力对极限环振荡的形式影响较小,但在精确预测颤振边界和极限环振荡现象时应考虑阻力的影响,算例研究结果表明极限环振荡对速度比较敏感.谢亮等[70]基于NASTRAN和CFD求解器,开发了一套基于CFD/CSD耦合求解的气动弹性时域仿真程序,并计算了切尖三角翼极限环振荡现象的动气动弹性仿真,结果表明结构非线性对气动弹性和极限环振荡有显著影响.赵振军[71]基于多体系统动力学对悬臂柔性机翼的气动弹性进行研究,并进一步分析了折叠间隙对折叠翼极限环响应的影响.肖艳平等[72]采用基于Wagner函数的非定常气动力, 考虑大展弦比机翼的几何大变形和机翼外挂系统的结构非线性, 运用伽辽金法进行离散, 对大展弦比机翼及机翼外挂系统的非线性响应进行了深入的研究, 分析了各种参数对系统颤振特性的影响以及系统发生分叉失稳的复杂运动形态.肖志鹏等[73]将机翼简化为复合材料板, 对机翼的颤振和气动弹性进行了优化分析.张伟等[74]考虑高阶横向剪切效应、几何大变形和横向阻尼的影响, 基于Reddy的高阶剪切变形理论和Von Karman的大变形理论, 利用Hamilton原理研究了复合材料层合悬臂板的非线性动力学问题.QIAO等[75]基于CFD/CSD建立了非线性颤振分析方法,可用于分析大变形引起的几何非线性问题.
3.3 气动弹性仿真框架开展柔性飞行器结构几何非线性、气动非线性等方面的气动弹性与飞行力学耦合问题的相关研究,需建立结构中等/大变形运动自由度与全机运动自由度的统一模型,对其耦合求解.随着大展弦比柔性长航时无人机相关问题的深入探索,国外逐渐衍生出若干柔性飞机非线性气动弹性与飞行力学耦合的仿真工具/框架.
ASWING可求解静平衡、频域和时域响应以及动稳定性等问题,具有一定的工程精度.Love等[76]利用ASWING研究了后掠翼飞翼布局传感器飞机的刚体自由颤振.GonzáLez等[77]基于ASWING建立了气动弹性模型并进行了静稳定性分析.但ASWING对连翼布局飞行器气动弹性的分析求解能力不足.
UM/NAST(The University of Michigan’s Nonlinear Simulation Toolbox)最初是由密歇根大学的Cesnik等[78-79]和Brown[80]建立的一套用于大展弦比柔性飞行器非线性气动弹性与飞行力学耦合的仿真框架,适用于常规、飞翼和连翼等多种布局形式.Su等[81]引入了阵风模型,并以双线性刚度模型考虑蒙皮褶皱效应,研究了柔性飞机的配平、纵向稳定性和阵风响应等;对连翼布局的边界约束进行改进,使用拉格朗日乘子法代替了法函数法[82];研究了BWB布局传感器飞机的固有振动特性、刚体自由颤振特性、刚柔耦合时域响应和阵风响应等[83].
国内针对柔性飞行器非线性气动弹性与飞行力学耦合分析的仿真工具尚不多见.其中,赵振军等[71, 84]基于多体动力学方法和ONERA-Edlin动失速气动力模型,研究了各种飞行状态下的时域响应,通过时域响应计算获得全机配平等系统静稳态解.张健等[85-86]建立了大展弦比柔性飞机非线性气动弹性与飞行力学的刚柔耦合模型,机身简化为刚体,机翼结构由具有大位移和大转动的运动梁建模,综合考虑了挂载和集中载荷等非连续因素.因此,建立一套能够完整地进行大展弦比柔性飞行器非线性气动弹性与飞行力学耦合分析的研究工具,充分考虑结构几何非线性、气动非线性以及结构弹性与飞行力学之间的非线性效应,具有一定的现实和工程意义.文献[86]当机翼垂直弯曲变形较小,铅垂方向上有效升力损失较小时,由于机翼扭转弹性变形对其局部迎角的贡献,柔性飞机配平迎角小于刚性飞机配平迎角;当机翼垂直弯曲变形较大,铅垂方向上有效升力损失较大时,柔性飞机配平迎角大于刚性飞机配平迎角,如图 2所示.针对完整非线性刚柔耦合的时域响应,机翼变形较小时,失速区域可能由翼根向翼尖扩展,翼展失速区域较大,全机升力损失显著,飞行高度迅速降低;机翼变形较大时, 失速首先发生于翼尖,而后向翼根扩展,失速范围有限,全机升力损失相对较小,如图 3、4所示.
Figure 2
![点击查看原图](http://hit.alljournals.cn/html/hitxb_cn/2017/10/PIC/hebgydxxb-49-10-1-2.jpg)
Figure 3
![点击查看原图](http://hit.alljournals.cn/html/hitxb_cn/2017/10/PIC/hebgydxxb-49-10-1-3.jpg)
Figure 4
![点击查看原图](http://hit.alljournals.cn/html/hitxb_cn/2017/10/PIC/hebgydxxb-49-10-1-4.jpg)
4 大展弦比复合材料机翼主动控制主动控制技术(active control technology, ACT)是一种通过控制器来消除气动弹性不稳定性的技术或方案,可广泛应用于多种飞行器,包括大展弦比机翼.主动控制技术可用于载荷减缓[87-89],用于阵风响应[90]、稳定性、极限环振荡以及经典的颤振抑制[91],不同控制器有各自对应的用途.
4.1 主动阵风减缓阵风减缓一直是大展弦比机翼的热点研究领域.飞行器在飞行中常会受到大气扰动以及机动操纵诱导载荷的影响而产生附加过载,其中垂直阵风的影响尤为显著[92].大展弦比柔性飞行器的非线性气动弹性特性使得其对阵风载荷尤为敏感,内部结构产生较大的应力载荷,因此有必要研究阵风载荷减缓的相关问题.
Shearer等[93-94]扩展了UM/NAST的刚体线性模型和非线性模型的时域仿真功能,在微分方程中引入了修改的Generalized时域积分算法[95],开展了柔性飞行器轨迹控制研究[96].BI等[97]针对大展弦比柔性机翼,利用压电制动器主动控制技术进行阵风载荷减缓.利用Hamilton原理推导压电材料柔性翼运动方程,数值求解阵风响应.利用经典的PID控制器进行阵风载荷减缓.杨俊斌等[98]针对大展弦比飞翼布局飞机,设计了风洞模型、沉浮-俯仰2自由度的支持系统以及能够产生连续正弦阵风的阵风发生器,采用经典控制律理论设计了能够同时减缓翼尖过载和翼根弯矩的3种控制方案,开展了阵风减缓主动控制风洞试验,并对开环、闭环试验数据进行了分析.
为了减缓阵风载荷的影响,飞行器通常安装阵风载荷减缓系统(gust load alleviation,GLA),或在飞行计算机中安装阵风减缓模块(loads alleviation function,LAF),通过控制面来改变飞行器的姿态进而达到阵风载荷减缓的效果,或利用传感器闭环控制,或利用飞控操纵控制.
Regan等[99]和Bray[100]通过LAF来实现阵风载荷减缓,上述设计多采用主动控制来实现.而对于无人机系统,主动阵风减缓控制势必会增加系统设计的复杂性,而且还需要加装传感器系统和应对操纵装置失效的余度系统,这势必增加结构质量,不利于航程扩展.因此,被动阵风减缓方式一直是重要的研究方向.Perron等[101-102]针对民机机翼,利用复合材料机翼铺层弯扭耦合设计降低阵风载荷.Vio等[103]基于传感器飞机利用复合材料气动剪裁实现阵风载荷减缓,并对复合材料铺层进行优化设计.Miller等[104]利用气动弹性减缩模型研究了连翼布局无人机被动阵风减缓,结果表明该装置能够有效地减缓阵风响应且对机翼的颤振特性影响较小.Guo等[105]利用有限元软件和解析方法研究了飞翼布局无人机的被动阵风减缓.
4.2 颤振主动控制大展弦比机翼颤振速度相对较低,基于颤振主动控制技术能有效提高大展弦比飞机的颤振速度,扩大大展弦比飞机的飞行包线.文献[84]研究了大展弦比柔性翼的飞行动力学、气动弹性和控制.文献[87]针对HALE机翼设计了一种SOF控制器用于阵风载荷减缓与极限环振荡抑制.文献[96]开发了一种针对大展弦比柔性翼的轨迹控制器.在文献[96]开发控制器的基础上,Dillsaver等[106]设计了一个针对大展弦比柔性翼轨迹控制的双层控制律.文献[89]针对HALE机翼,研究了阵风载荷减缓和沉浮模态稳定性的后缘舵面控制器.Wang等[107]针对大展弦比柔性翼在模态坐标中的飞行仿真,研究了一种非线性气动弹性伺服方案.文献[91]基于IST航空航天集团的非线性气动弹性框架,设计了抑制大展弦比机翼气弹失稳的控制律.
5 大展弦比复合材料机翼气动弹性剪裁纤维铺层复合材料具有高强度、高弹性模量、各向异性等特点,通过改变铺层角度、层数以及铺层顺序,可以获得满足对应要求的材料性能,这种特性为大展弦比机翼的优化提供了很高的可设计性.气动弹性剪裁优化的目标为减轻质量、减少阻力、改善阵风响应、优化颤振特性,以及上述目标的综合化结果,从而改善机翼的刚度和机翼弯扭变形的被动弹性耦合,提高翼面的颤振、发散速度,改善机翼的气动弹性性能.
由于大展弦比复合材料机翼具有显著的几何非线性特征,且在结构设计中有低质量的要求,在优化设计中具有设计变量多,影响因素复杂的特点.采用合理的算法与优化策略,并结合复合材料的特性,可以在最小质量约束前提下极大地提高机翼性能.
在大展弦比复合材料机翼优化中,质量通常被设定为目标函数.约束条件是机翼在外部载荷作用下的强度条件、刚度条件或其他性能指标.对于机翼的质量优化,所采用的方法是在尽可能减少质量增加量的前提下,对复合材料铺层进行合理的剪裁.传统的大展弦比复合材料机翼优化方法包括敏度算法[63]、遗传算法[108]等,也包括各算法的复合应用,如万志强等[109]以机翼各结构铺层厚度为变量,以结构质量最小化为目标的遗传敏度混合设计方法.Macquart等[110]采用混合约束法对复合材料铺层角度与厚度进行优化,从而求出每一层的属性,进一步汇同截面求出铁摩辛柯梁刚度矩阵.Liu等[111]对于设计变量的变化性,对总体布局-局部材料铺层两个目标函数采用并行优化法,显著减小了复合材料机翼结构的质量优化结果因不确定变量产生的误差.
机翼的颤振临界速度作为飞行器飞行包线的边界之一,也是一个比较重要的优化设计参数,由于大展弦比柔性机翼的颤振临界速度相对较低,通常也作为目标函数对结构进行优化.对于多目标、不同目标包含各自的约束条件的优化,往往采用二级或多级优化法,即每一级设定不同的目标函数,并以上一级的结果作为约束条件带入下一级优化中.这种以分步的、并行的局部优化构成整体优化的方法,需要设定合理的优化策略,使优化的结果更接近最优解.如Guo等[112]将机翼翼盒的结构质量设定为目标函数,将蒙皮层数和铺层角度作为设计变量,求得质量最优解后,将结果带入阵风响应减缓条件中,通过使铺层角度-层数的顺序增加,逐步提高机翼刚度,最后完成气动弹性剪裁优化.白俊强等[113]提出了三级优化法,以质量为目标函数,在满足静强度的条件下进行结构优化后,以颤振速度为约束条件对铺层比例优化,再进行铺层顺序优化,通过对铺层参数的调整,在不改变质量的情况下进一步提高颤振速度.Yang等[114]基于响应面法对大展弦比复合材料机翼进行多目标遗传算法优化.
近年来,随着优化算法在大展弦比复合材料机翼上应用的不断拓展,与传统的优化法相比,采用现代优化算法的算例在收敛速度以及精确度上有了很大的提高.Wan等[115]验证了采用粒子群算法(PSO)的优化方法,该方法是一种模拟鸟类觅食策略的进化算法,在求得一个随机的,非优化的目标后,通过评估、迭代找到最优解,收敛速度非常快.文献[113]提出一种基于BLISS算法的混合多级结构优化算法,通过静强度优化-铺层比例优化-铺层顺序优化的逐级优化法减少每一级中不必要的约束,从而减少约束个数和运算次数,达到快速运算的目的.
除了算法的应用,优化方法也与近年来气动弹性新的发展方向相结合,例如Alyanak等[116]提出了将机翼进行气动弹性剪裁后,再进行主动气动弹性方面的优化,给予了复合材料大展弦比机翼优化的新的思路与方向.
6 大展弦比复合材料机翼试验大展弦比复合材料机翼的试验研究内容包括:非线性气动弹性影响, 例如极限环震荡[54, 117]、阵风响应[118-120]、非线性气动弹性响应[121],同时验证数值计算的有效性.
风洞试验的安装机制需要精确的设置与校正,不同的支持系统取决于不同类型的气动弹性测试试验.Su等[122]在大展弦比柔性翼的研究中,采用结构动模态与刚体模态的耦合效应,这会导致自由颤振,由于飞行器被约束,所以该现象在传统风洞中不可观测.传统风洞试验不适用于该类型的飞行器,Tang等[123]提出了一种模拟刚体模态的柔性支持系统.
文献[117-119]针对带有翼尖细长体的大展弦比柔性机翼,进行了颤振边界预测、极限环振荡、阵风响应等方面的风洞试验研究.基于Hodges-Dowell非线性梁模型开展了相应的理论分析,利用时域仿真和谐波平衡法分析了试验模型的极限环迟滞响应特性,理论结果与试验吻合较好, 研究揭示了机翼根部攻角和几何非线性对颤振边界、极限环振荡、突风响应的影响规律,指出机翼的几何非线性主要依赖于展向与弦向弯曲刚度之比.Dowell等[124]对其非线性气动弹性的建模理论、计算分析以及试验能力进行了阶段性的回顾与总结.
Dietz等[125]针对大展弦比后掠机翼的极限环振荡进行了风洞试验研究,发现在机翼未发生流动分离时也会出现低幅值的极限环振荡现象,针对这一现象,Bendiksen等[126]基于CFD方法对大展弦比后掠机翼的极限环振荡进行了研究,并与文献[125]风洞试验吻合较好,指出后掠机翼具有“洗脱”(washout)效应,其有效攻角在沿展向从翼根到翼尖逐渐减小,影响极限环振荡的发生.Cesnik等[127-128]制作了大展弦比长航时飞翼无人机模型X-HALE,旨在开展非线性气动弹性飞行测试,为柔性飞机非线性气动弹性与飞行力学耦合仿真工具提供试验支持.
Liu等[129]提出了一种预测大展弦比柔性翼几何非线性阵风响应的多学科耦合的数值计算方法,并在风洞试验中采用新型非接触三维相机测量分析系统,进而获得空间大变形和响应,数值计算与风洞试验结果吻合较好.谢长川等[18, 130-131]利用结构/气动界面耦合的曲面插值方法,耦合结构和气动力模型,开展了面向工程应用的实例研究与风洞试验,并基于静态变形平衡位置附近小幅振动的“准模态法”假设,提出了考虑几何非线性的大展弦比柔性飞机非线性气动弹性稳定性分析的线性化方法,分析结构几何非线性对大展弦比机翼振动特性的影响.
7 结论1) 现有大展弦比复合材料机翼的结构模型多采用等效梁板模型,大大提高了计算分析效率.
2) 现有大展弦比复合材料机翼的气动模型多采用片条理论与考虑动失速的二元非定常气动力相结合的模型,可以较为准确地描述大展弦比机翼的气动特性.
3) 基于CFD的气动降阶模型可以计算不同马赫数以及气动失速情况下的气动力,且具备较高的计算精度和计算效率,该方法耦合大展弦比复合材料机翼结构模型,进行气动弹性分析、控制律设计、气动弹性剪裁等,是大展弦比复合材料机翼研究的发展方向之一.
4) 现有大展弦比复合材料机翼的研究大多停留在理论研究与地面试验阶段,飞行试验数据较少,因此,飞行试验是大展弦比复合材料机翼研究的重要方向之一.
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