旋翼动态失速与反流流动控制研究进展

李国强; 赵鑫海; 易仕和; 宋奎辉; 赵光银

doi:10.11729/syltlx20230054

旋翼动态失速与反流流动控制研究进展

doi: 10.11729/syltlx20230054

李国强^{1, 2,},
赵鑫海^2, ,,
易仕和¹,
宋奎辉²,
赵光银²

1.
国防科技大学空天科学学院，长沙　410073
2.
中国空气动力研究与发展中心低速空气动力研究所，绵阳　621000

基金项目: 预先研究项目（50906030601）；综合研究项目（JK20211A020092）

详细信息

作者简介:
李国强：（1987—），男，安徽蚌埠人，硕士，工程师。研究方向：直升机空气动力学，主动流动控制技术。通信地址：四川省绵阳市涪城区二环路南段6号13 信箱（621000）。E-mail：CARDCL@126.com

通讯作者:
E-mail：18773129527@163.com

中图分类号: V211.4
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- 文章访问数: 150
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- 被引次数: 0
出版历程
- 收稿日期: 2023-04-13
- 修回日期: 2023-05-24
- 录用日期: 2023-05-26
- 网络出版日期: 2023-07-31
- 刊出日期: 2023-08-30

Research progress on rotor reverse flow and dynamic stall flow control methods

1.
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha　410073, China
2.
Low Speed Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang　621000, China

摘要

摘要: 直升机在大载荷高速前飞时，旋翼桨叶桨距变化较大，易发生动态失速；后行桨叶内段旋转线速度较低，在来流叠加下形成反流区，导致桨叶气动效率降低，由此产生的桨叶疲劳失效和升力下降问题阻碍直升机性能的进一步提升。流动控制方法在改善翼型气动特性方面具有较大潜能，是提升旋翼气动效率、保障直升机安全的有效路径之一。本文阐述了旋翼反流区和动态失速的形成机理及非定常流动特征，综述了2种特殊气动现象的研究成果。对比分析了优化翼型几何构型、添加表面机械结构、吹气控制、等离子体控制、合成射流控制和后缘小翼控制等流动控制方法对旋翼动态失速及反流控制的机理，总结了控制参数和流场参数对控制效果的影响规律，分析了各种方法在应用中存在的问题，对发展方向进行了展望。
- 旋翼 /
- 动态失速 /
- 反流 /
- 流动控制
Abstract: When a helicopter flies forward at high speed with heavy load, the blade pitch changes greatly and dynamic stall is prone to occur. The lower rotational speed of the inner section of the trailing blade leads to the formation of a reverse flow zone under the superposition of the incoming flow, resulting in a reduction in the aerodynamic efficiency of the blade. The problems of blade fatigue failure and lift reduction hinder the further improvement of helicopter performance. Flow control methods have great potential in improving the aerodynamic characte-ristics of airfoils, and are effective ways to improve the rotor aerodynamic efficiency and ensure helicopter safety and stability. In this paper, the formation mechanism and unsteady flow characteristics of the reverse flow zone and dynamic stall are firstly described, and the research results of two special aerodynamic phenomena are summarized. On this basis, a comparative analysis of flow control methods such as variable airfoil configuration, surface mechanical devices, air-blowing control, plasma actuator, synthetic jet actuator, and trailing edge flap on the mechanism of rotor dynamic stall and reverse flow control is conducted, and the effects of control parameters and flow field parameters on control effectiveness are summarized. Finally, the remain-ing problems and solutions in the application of various flow control methods are prospected.
- rotorcraft /
- dynamic stall /
- reverse flow /
- flow control

HTML全文

图 1 不同前进比对应的反流区示意图

Figure 1. Reverse region with different μ

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图 2 典型状态下直升机桨叶剖面阻力系数分布^[10]

Figure 2. Distribution of resistance coefficient of helicopter blade under typical conditions^[10]

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图 3 翼型俯仰运动对升力系数的影响^[14]

Figure 3. Effect of airfoil pitching motion on lift coefficient^[14]

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图 4 带后掠角翼型的表面流动^[19]

Figure 4. Surface flow of airfoil with sweepback angle^[19]

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图 5 钝后缘翼型在反流中的流动显示结果^[28]

Figure 5. Flow visualization of blunt tail airfoil in reverse flow^[28]

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图 6 X2TD和XH–59A桨叶根部翼型对比^[25]

Figure 6. Comparison of propeller shank between X2TD and XH–59A^[25]

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图 7 座头鲸鳍肢^[32]

Figure 7. Flipper of a humpback whale^[32]

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图 8 正弦前缘产生的流动结构示意图^[35]

Figure 8. Schematic of flow structures produced by sinusoidal leading edge^[35]

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图 9 涡流发生器对升力系数的影响^[42]

Figure 9. Impact of VGs on lift coefficient^[42]

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图 10 2种规格的片状涡流发生器阵列^[44]

Figure 10. Two arrays of VGs^[44]

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图 11 带扰流板的翼型^[46]

Figure 11. Airfoil with spoiler^[46]

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图 12 襟翼处狭缝吹气示意图^[59]

Figure 12. Schematic of flap blowing slot^[59]

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图 13 沿展向排列的吹气孔阵列^[61]

Figure 13. Array of blowing holes along the spanwise direction^[61]

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图 14 协同射流结构简图^[67]

Figure 14. Schematic of CFJ^[67]

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图 15 布置于翼梢附近的协同射流控制系统^[71]

Figure 15. CFJ near the wing tip^[71]

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图 16 交流等离子体激励器结构示意图^[77]

Figure 16. Schematic of AC–DBD^[77]

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图 17 AC–DBD和NS–DBD示意图^[84]

Figure 17. AC–DBD and NS–DBD^[84]

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图 18 合成射流激励器示意图^[89]

Figure 18. Schematic of synthetic jet^[89]

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图 19 合成射流作用下的翼型表面丝线流动显示结果^[103]

Figure 19. Surface flow visualization of airfoil under the control of synthetic jet^[103]

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图 20 合成双射流激励器结构示意及PIV试验结果^[104]

Figure 20. Schematic of dual synthetic jet and its related PIV result^[104]

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图 21 固定偏转角度的后缘小翼^[107]

Figure 21. Trailing winglet with fixed defection angle^[107]

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图 22 后缘小翼对俯仰力矩系数的影响（红色实线：带控制）^[107]

Figure 22. Pitching moment change by trailing winglet (red solid line)^[107]

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图 23 20°后掠角翼型表面流线^[111]

Figure 23. Surface flow of airfoil with 20° sweepback angle^[111]

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图 24 带后缘小翼的模型^[117]

Figure 24. Airfoil with active trailing winglet^[117]

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图 25 翼型和小翼偏转角控制方式^[118]

Figure 25. Controlling strategy of airfoil and trailing winglet^[118]

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图 26 鱼骨形机翼^[128]

Figure 26. Fishbone airfoil^[128]

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图 27 鱼骨形后缘小翼^[130]

Figure 27. Fishbone trailing winglet^[130]

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表 1 旋翼系统流动控制方法对比

Table 1. Comparison of flow methods for rotor system

流动控制方法	控制原理	主要优点	主要缺点	实现难易度	应用于旋翼的案例
优化翼型几何构型	改变翼型升阻特性	结构简单，稳定可靠	非定常状态控制效率低	容易	H160直升机^[24]，验证机X2TD^[25]
添加表面机械结构	改变边界层能量分布和外部流场结构	结构简单，稳定可靠	非定常状态控制效率低，产生“废阻”多	主动式控制较难	EC−145^[26]
吹气控制	注入高能射流	控制效率高	系统结构复杂	供气系统难实现	仅有专利
等离子体控制	电场诱导射流	结构简单，体积小	极端环境适应力弱，能效比低	电源和控制系统较难实现	仅有专利
合成射流控制	振动腔赋能射流	无需气源	极端环境适应力弱，高速条件下控制效率低	复杂流场下较难实现	仅有专利
后缘小翼控制	改变外部流场结构	控制效率高	控制机构和策略待优化	主动式控制较难	MD900风洞模型^[27]

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参考文献(131)

[1]	LEISHMAN G J Principles of helicopter aerodynamics with CD extra[M]. 2nd edition. Cambridge: Cambridge University Press, 2006.
[2]	张卫国, 李国强, 李栋, 等. 旋翼翼型动态风洞试验技术研究[J]. 实验流体力学, 2023, 37(2): 78–93. doi: 10.11729/syltlx20210147 ZHANG W G, LI G Q, LI D, et al. Research on dynamic wind tunnel testing of rotor airfoil[J]. Journal of experiments in fluid mechanics, 2023, 37(2): 78–93. doi: 10.11729/syltlx20210147
[3]	SANTRA S, GREENBLATT D. Dynamic stall control model for pitching airfoils with slot blowing[J]. AIAA Journal, 2021, 59(1): 400–404. doi: 10.2514/1.J059818
[4]	张卫国, 李国强, 宋奎辉, 等. 旋翼翼型高速风洞动态试验装置研制[J]. 工程设计学报, 2022, 29(4): 500–509. doi: 10.3785/j.issn.1006-754X.2022.00.056 ZHANG W G, LI G Q, SONG K H, et al. Development of dynamic test equipment for rotor airfoil in high speed wind tunnel[J]. Chinese Journal of Engineering Design, 2022, 29(4): 500–509. doi: 10.3785/j.issn.1006-754X.2022.00.056
[5]	史志伟, 耿存杰, 明晓, 等. 旋翼翼型俯仰沉浮运动非定常气动特性实验研究[J]. 实验流体力学, 2007, 21(3): 18–23. doi: 10.3969/j.issn.1672-9897.2007.03.004 SHI Z W, GENG C J, MING X, et al. Experimental investigation on unsteady aerodynamics of rotor-blade airfoil[J]. Journal of Experiments in Fluid Mechanics, 2007, 21(3): 18–23. doi: 10.3969/j.issn.1672-9897.2007.03.004
[6]	BAILEY F J, Jr, GUSTAFSON F B. Observations in flight of the region of stalled flow over the blades of an autogiro rotor[R]. NACA-TN-741, 1939.
[7]	DATTA A, YEO H, NORMAN T R. Experimental investigation and fundamental understanding of a full-scale slowed rotor at high advance ratios[J]. Journal of the American Helicopter Society, 2013, 58(2): 1–17. doi: 10.4050/jahs.58.022004
[8]	袁明川, 杨永飞, 林永峰. 高速直升机旋翼反流区桨叶剖面翼型气动特性CFD分析[J]. 直升机技术, 2015(1): 1–5, 12. doi: 10.3969/j.issn.1673-1220.2015.01.001 YUAN M C, YANG Y F, LIN Y F. CFD analysis on aerodynamic characteristics of blade profiles in reverse flow region of high speed helicopter rotor[J]. Helicopter Technique, 2015(1): 1–5, 12. doi: 10.3969/j.issn.1673-1220.2015.01.001
[9]	HASSAN A A, STRAUB F K, NOONAN K W. Experimental/numerical evaluation of integral trailing edge flaps for helicopter rotor applications[J]. Journal of the American Helicopter Society, 2005, 50(1): 3–17. doi: 10.4050/1.3092838
[10]	孔卫红, 陈仁良. 反流区对复合高速直升机旋翼气动特性的影响[J]. 航空学报, 2011, 32(2): 223–230. KONG W H, CHEN R L. Effect of reverse flow region on characteristics of compound high speed helicopter rotor[J]. Acta Aeronautica et Astronautica Sinica, 2011, 32(2): 223–230.
[11]	LIND A H, SMITH L R, MILLUZZO J I, et al. Reynolds number effects on rotor blade sections in reverse flow[J]. Journal of Aircraft, 2016, 53(5): 1248–1260. doi: 10.2514/1.C033556
[12]	MABEY D. Some aspects of aircraft dynamic loads due to flow separation[J]. Progress in Aerospace Sciences, 1989, 26(2): 115–151. doi: 10.1016/0376-0421(89)90006-7
[13]	WILLIAMSON C H K, GOVARDHAN R. Vortex-induced vibrations[J]. Annual Review of Fluid Mechanics, 2004, 36: 413–455. doi: 10.1146/annurev.fluid.36.050802.122128
[14]	GARDNER A D, JONES A R, MULLENERS K, et al. Review of rotating wing dynamic stall: experiments and flow control[J]. Progress in Aerospace Sciences, 2023, 137: 100887. doi: 10.1016/j.paerosci.2023.100887
[15]	ZHU C Y, QIU Y N, WANG T G. Dynamic stall of the wind turbine airfoil and blade undergoing pitch oscillations: a comparative study[J]. Energy, 2021, 222: 120004. doi: 10.1016/j.energy.2021.120004
[16]	陈恺, 张震宇, 王同光. 反流及径向流动相互作用下刚性旋翼气动特性研究[J]. 南京航空航天大学学报, 2019, 51(2): 187–193. doi: 10.16356/j.1005-2615.2019.02.008 CHEN K, ZHANG Z Y, WANG T G. Numerical study of sweep effect on aerodynamic characteristics of helicopter rotor blade in reverse flow[J]. Journal of Nanjing University of Aeronautics & Astronautics, 2019, 51(2): 187–193. doi: 10.16356/j.1005-2615.2019.02.008
[17]	钱宇, 蒋皓. 基于动网格技术的机翼动态失速仿真分析[J]. 科学技术与工程, 2021, 21(15): 6501–6505. doi: 10.3969/j.issn.1671-1815.2021.15.055 QIAN Y, JIANG H. Simulation analysis of wing dynamic stall based on dynamic mesh technology[J]. Science Technology and Engineering, 2021, 21(15): 6501–6505. doi: 10.3969/j.issn.1671-1815.2021.15.055
[18]	CARTA M, PUTZU R, GHISU T. A comparison of plunging- and pitching-induced deep dynamic stall on an SD7003 airfoil using URANS and LES simulations[J]. Aerospace Science and Technology, 2022, 121: 107307. doi: 10.1016/j.ast.2021.107307
[19]	RAGHAV V, MAYO M, LOZANO R, et al. Evidence of vortex-induced lift on a yawed wing in reverse flow[J]. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2014, 228(11): 2130–2137. doi: 10.1177/0954410013511597
[20]	SMITH L R, JONES A R. Measurements on a yawed rotor blade pitching in reverse flow[J]. Physical Review Fluids, 2019, 4(3): 034703. doi: 10.1103/physrevfluids.4.034703
[21]	谢凯, ABBAS L K, 陈东阳, 等. 翼型非定常来流下复合运动动态失速仿真[J]. 哈尔滨工程大学学报, 2019, 40(5): 865–871. doi: 10.11990/jheu.201711100 XIE K, ABBAS L K, CHEN D Y, et al. Numerical simulations on dynamic stall of a complex motion of airfoil under unsteady freestream velocity[J]. Journal of Harbin Engineering University, 2019, 40(5): 865–871. doi: 10.11990/jheu.201711100
[22]	CRITZOS C C, HEYSON H H, BOSWINKLE R W, Jr. Aerodynamic characteristics of NACA 0012 airfoil section at angles of attack from 0° to 180°[R]. NACA-TN-3361, 1955.
[23]	SMITH M J. An assessment of the state-of-the-art from the 2019 ARO dynamic stall workshop[C]//Proc of the AIAA Aviation 2020 Forum. 2020: 2697. doi: 10.2514/6.2020-2697
[24]	HICKS M A, BARBER A E II, BABBITT P C. The nucleophilic attack six-bladed β-propeller (N6P) super-family[M]//ORENGO C, BATEMAN A. Protein Families: Relating Protein Sequence, Structure, and Function. NJ, USA: John Wiley & Sons, Inc., 2013: 125-158. doi: 10.1002/9781118743089.ch6
[25]	BAGAI A. Aerodynamic design of the X2 technology demonstrator™ main rotor blade[J]. Annual Forum Proceedings - American Helicopter Society, 2008, 64(1): 29.
[26]	ASHTON N, BILLARD F, MOULINEC C, et al. The numerical simulation of the flow over a EC145 helicopter fuselage using HPC facilities[C]//Proc of the 23rd International Conference on Parallel Computational Fluid Dynamics. 2011.
[27]	SHEN J W, CHOPRA I. A parametric design study for a swashplateless helicopter rotor with trailing-edge flaps[J]. Journal of the American Helicopter Society, 2004, 49(1): 43–53. doi: 10.4050/jahs.49.43
[28]	LIND A H, LEFEBVRE J N, JONES A R. Time-averaged aerodynamics of sharp and blunt trailing-edge static airfoils in reverse flow[J]. AIAA Journal, 2014, 52(12): 2751–2764. doi: 10.2514/1.J052967
[29]	LIND A H, JONES A R. Vortex shedding from airfoils in reverse flow[J]. AIAA Journal, 2015, 53(9): 2621–2633. doi: 10.2514/1.J053764
[30]	LIND A H, JONES A R. Unsteady aerodynamics of reverse flow dynamic stall on an oscillating blade section[J]. Physics of Fluids, 2016, 28(7): 077102. doi: 10.1063/1.4958334
[31]	厉聪聪, 史勇杰, 徐国华, 等. 基于动态前缘下垂的提升旋翼前飞性能的研究[J]. 西北工业大学学报, 2021, 39(3): 668–674. doi: 10.3969/j.issn.1000-2758.2021.03.025 LI C C, SHI Y J, XU G H, et al. Research on the forward flight performance of rotor based on variable-droop leading edge[J]. Journal of Northwestern Polytechnical University, 2021, 39(3): 668–674. doi: 10.3969/j.issn.1000-2758.2021.03.025
[32]	蔡畅. 仿座头鲸鳍肢前缘凸起对翼型失速特性控制机理研究[D]. 北京: 清华大学, 2018: 105-106. CAI C. Effects of leading-edge protuberances inspired by humpback whale flipper on airfoil stall control[D]. Beijing: Tsinghua University, 2018: 105-106. doi: 10.27266/d.cnki.gqhau.2018.000320
[33]	侯宇飞, 李志平. 仿生正弦前缘对翼面动态失速的影响[J]. 航空学报, 2020, 41(1): 139–151. doi: 10.7527/S1000-6893.2019.23276 HOU Y F, LI Z P. Effect of bionic sinusoidal leading-edge on dynamic stall of airfoil[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(1): 139–151. doi: 10.7527/S1000-6893.2019.23276
[34]	张一楠. 仿鲸鱼鳍风力机翼型气动力性能控制研究[D]. 北京: 中国科学院大学, 2020: 131-132. ZHANG Y N. Research on aerodynamic performance control of wind turbine airfoil with leading-edge protuberances[D]. Beijing: University of Chinese Academy of Sciences, 2020: 131-132.
[35]	HRYNUK J T, BOHL D G. The effects of leading-edge tubercles on dynamic stall[J]. Journal of Fluid Mechanics, 2020, 893: A5. doi: 10.1017/jfm.2020.216
[36]	LU Y, LI Z Y, CHANG X, et al. An aerodynamic optimization design study on the bio-inspired airfoil with leading-edge tubercles[J]. Engineering Applications of Computational Fluid Mechanics, 2021, 15(1): 292–312. doi: 10.1080/19942060.2020.1856723
[37]	吴立明, 姜怡欣, 刘小民, 等. 几种仿生翼型动态失速特性的数值分析[J]. 西安交通大学学报, 2022, 56(9): 1–9. doi: 10.7652/xjtuxb202209001 WU L M, JIANG Y X, LIU X M, et al. Numerical analysis of dynamic stall characteristics of several bionic airfoils[J]. Journal of Xi’an Jiaotong University, 2022, 56(9): 1–9. doi: 10.7652/xjtuxb202209001
[38]	LIU J, CHEN R, LOU J, et al. Deep-learning-based aerodynamic shape optimization of rotor airfoils to suppress dynamic stall[J]. Aerospace Science and Technology, 2023, 133: 108089. doi: 10.1016/j.ast.2022.108089
[39]	褚胡冰, 张彬乾, 陈迎春, 等. 微型涡流发生器控制增升装置流动分离研究[J]. 西北工业大学学报, 2011, 29(5): 799–805. doi: 10.3969/j.issn.1000-2758.2011.05.026 CHU H B, ZHANG B Q, CHEN Y C, et al. Controlling flow separation of high lift transport aircraft with micro vortex generators[J]. Journal of Northwestern Polytechnical University, 2011, 29(5): 799–805. doi: 10.3969/j.issn.1000-2758.2011.05.026
[40]	HEINE B, MULLENERS K, JOUBERT G, et al. Dynamic stall control by passive disturbance generators[J]. AIAA Journal, 2013, 51(9): 2086–2097. doi: 10.2514/1.J051525
[41]	赵振宙, 孟令玉, 王同光, 等. 涡流发生器对风力机翼段动态失速影响[J]. 哈尔滨工程大学学报, 2021, 42(2): 233–239. doi: 10.11990/jheu.201908076 ZHAO Z Z, MENG L Y, WANG T G, et al. Influence of vortex generators on dynamic stall of wind turbine airfoil segment[J]. Journal of Harbin Engineering University, 2021, 42(2): 233–239. doi: 10.11990/jheu.201908076
[42]	LI S, ZHANG L, XU J, et al. Experimental investigation of a pitch-oscillating wind turbine airfoil with vortex generators[J]. Journal of Renewable and Sustainable Energy, 2020, 12(6): 063304. doi: 10.1063/5.0013300
[43]	赵振宙, 孟令玉, 苏德程, 等. 涡流发生器形状对风力机翼段动态失速的影响[J]. 工程热物理学报, 2021, 42(8): 1989–1996. ZHAO Z Z, MENG L Y, SU D C, et al. Effect of vortex generator shape on dynamic stall of wind turbine airfoil[J]. Journal of Engineering Thermophysics, 2021, 42(8): 1989–1996.
[44]	DE TAVERNIER D, FERREIRA C, VIRÉ A, et al. Controlling dynamic stall using vortex generators on a wind turbine airfoil[J]. Renewable Energy, 2021, 172: 1194–1211. doi: 10.1016/j.renene.2021.03.019
[45]	NAIR N J, GOZA A. Fluid-structure interaction of a bio-inspired passively deployable flap for lift enhancement[J]. Physical Review Fluids, 2022, 7(6): 064701. doi: 10.1103/physrevfluids.7.064701
[46]	KAUFMANN K, GARDNER A D, RICHTER K. Numerical investigations of a back-flow flap for dynamic stall control[M]//DILLMANN A, HELLER G, KRÄMER E, et al. New results in numerical and experimental fluid mechanics IX. Cham: Springer International Publishing, 2014: 255-262. doi: 10.1007/978-3-319-03158-3_26
[47]	余海洋, 耿海超, 罗大海. 回流襟翼控制S809翼型动态失速的数值模拟研究[J]. 热能动力工程, 2020, 35(11): 127–134. doi: 10.16146/j.cnki.rndlgc.2020.11.019 YU H Y, GENG H C, LUO D H. Numerical investigation of a back-flow flap control for S809 airfoil dynamic stall[J]. Journal of Engineering for Thermal Energy and Power, 2020, 35(11): 127–134. doi: 10.16146/j.cnki.rndlgc.2020.11.019
[48]	薛世成, 缪维跑, 李春, 等. 尾缘气动弹片对翼型动态失速特性影响研究[J]. 热能动力工程, 2021, 36(12): 142–150. doi: 10.16146/j.cnki.rndlgc.2021.12.021 XUE S C, MIAO W P, LI C, et al. Effect of trailing edge aerodynamic flap on dynamic stall characteristics of airfoil[J]. Journal of Engineering for Thermal Energy and Power, 2021, 36(12): 142–150. doi: 10.16146/j.cnki.rndlgc.2021.12.021
[49]	李根, 缪维跑, 李春, 等. 凹槽-襟翼对翼型动态失速特性影响研究[J]. 热能动力工程, 2022, 37(3): 151–159. doi: 10.16146/j.cnki.rndlgc.2022.03.022 LI G, MIAO W P, LI C, et al. Effect of trailing edge dimple-flap on dynamic stall characteristics of airfoil[J]. Journal of Engineering for Thermal Energy and Power, 2022, 37(3): 151–159. doi: 10.16146/j.cnki.rndlgc.2022.03.022
[50]	OPITZ S, GARDNER A D, KAUFMANN K. Aerodynamic and structural investigation of an active back-flow flap for dynamic stall control[J]. CEAS Aeronautical Journal, 2014, 5(3): 279–291. doi: 10.1007/s13272-014-0106-3
[51]	向斌, 缪维跑, 李春, 等. 翼型前缘的气动滑片对动态失速特性的影响分析[J]. 动力工程学报, 2020, 40(9): 765–772. XIANG B, MIAO W P, LI C, et al. Effects of leading edge aerodynamic sliding vane on dynamic stall characteristics of the airfoil[J]. Journal of Chinese Society of Power Engineering, 2020, 40(9): 765–772.
[52]	SALIMIPOUR E, YAZDANI S, GHALAMBAZ M. Simulation of airfoil dynamic stall suppression with a burst control blade in a transitional flow regime[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2022, 44(8): 1–12. doi: 10.1007/s40430-022-03690-w
[53]	张馨艺, 孙晓晶. 带局部运动表面翼型的动态失速特性研究[J]. 动力工程学报, 2022, 42(9): 821–828. doi: 10.19805/j.cnki.jcspe.2022.09.005 ZHANG X Y, SUN X J. Study on dynamic stall characteristics of the airfoil with locally moving surface[J]. Journal of Chinese Society of Power Engineering, 2022, 42(9): 821–828. doi: 10.19805/j.cnki.jcspe.2022.09.005
[54]	WYGNANSKI I, NEWMAN B G. The effect of jet entrainment on lift and moment for a thin aerofoil with blowing[J]. Aeronautical Quarterly, 1964, 15(2): 122–150. doi: 10.1017/s0001925900003085
[55]	YU Y H, LEE S, McALISTER K W, et al. Dynamic stall control for advanced rotorcraft application[J]. AIAA Journal, 1995, 33(2): 289–295. doi: 10.2514/3.12496
[56]	CHEESEMAN I C, SEED A R. The application of circulation control by blowing to helicopter rotors[J]. The Aeronautical Journal, 1967, 71(679): 451–467. doi: 10.1017/s0001924000055238
[57]	WEAVER D, MCALISTER K, TSO J. Suppression of dynamic stall by steady and pulsed upper-surface blowing[C]//Proc of the 16th AIAA Applied Aerodynamics Conference. 1998: 2413. doi: 10.2514/6.1998-2413
[58]	SINGH C, PEAKE D J, KOKKALIS A, et al. Control of rotorcraft retreating blade stall using air-jet vortex generators[J]. Journal of Aircraft, 2006, 43(4): 1169–1176. doi: 10.2514/1.18333
[59]	SEIFERT A, DARABI A, WYGANSKI I. Delay of airfoil stall by periodic excitation[J]. Journal of Aircraft, 1996, 33(4): 691–698. doi: 10.2514/3.47003
[60]	NISHRI B, WYGNANSKI I. Effects of periodic excitation on turbulent flow separation from a flap[J]. AIAA Journal, 1998, 36(4): 547–556. doi: 10.2514/2.428
[61]	GARDNER A D, RICHTER K, MAI H, et al. Experimental investigation of air jets for the control of compressible dynamic stall[J]. Journal of the American Helicopter Society, 2013, 58(4): 1–14. doi: 10.4050/jahs.58.042001
[62]	GARDNER A D, RICHTER K, MAI H, et al. Experimental investigation of high-pressure pulsed blowing for dynamic stall control[J]. CEAS Aeronautical Journal, 2014, 5(2): 185–198. doi: 10.1007/s13272-014-0099-y
[63]	MÜLLER-VAHL H F, STRANGFELD C, NAYERI C N, et al. Control of thick airfoil, deep dynamic stall using steady blowing[J]. AIAA Journal, 2014, 53(2): 277–295. doi: 10.2514/1.J053090
[64]	RAMOS B L O, WOLF W R, YEH C A, et al. Active flow control for drag reduction of a plunging airfoil under deep dynamic stall[J]. Physical Review Fluids, 2019, 4(7): 074603. doi: 10.1103/physrevfluids.4.074603
[65]	MATALANIS C G, MIN B Y, BOWLES P O, et al. Combustion-powered actuation for dynamic-stall suppres-sion: high-Mach simulations and low-Mach experiments[J]. AIAA Journal, 2015, 53(8): 2151–2163. doi: 10.2514/1.J053641
[66]	CRITTENDEN T M, WOO G T K, GLEZER A. Combustion-powered actuation for transitory flow control[J]. AIAA Journal, 2018, 56(9): 3414–3435. doi: 10.2514/1.J056783
[67]	ZHA G C, PAXTON C D. A novel airfoil circulation augment flow control method using co-flow jet[C]//Proc of the 2nd AIAA Flow Control Conference. 2004: 2208. doi: 10.2514/6.2004-2208
[68]	ZHA G C, CARROLL B F, PAXTON C D, et al. High-performance airfoil using coflow jet flow control[J]. AIAA Journal, 2007, 45(8): 2087–2090. doi: 10.2514/1.20926
[69]	ZHA G C, YANG Y C, REN Y, et al. Super-lift and thrusting airfoil of coflow jet actuated by micro-compressors[C]//Proc of the 2018 Flow Control Conference. 2018: 3061. doi: 10.2514/6.2018-3061
[70]	LIU J Q, CHEN R Q, YOU Y C, et al. Numerical investigation of dynamic stall suppression of rotor airfoil via improved co-flow jet[J]. Chinese Journal of Aeronautics, 2022, 35(3): 169–184. doi: 10.1016/j.cja.2021.07.041
[71]	LIU J Q, CHEN R Q, SONG Q C, et al. Active flow control of helicopter rotor based on coflow jet[J]. International Journal of Aerospace Engineering, 2022, 2022: 1–19. doi: 10.1155/2022/9299470
[72]	许和勇, 马成宇. 协同射流流动控制方法研究进展综述[J]. 航空工程进展, 2022, 13(6): 1–16. doi: 10.16615/j.cnki.1674-8190.2022.06.01 XU H Y, MA C Y. Review of the Co-flow jet flow control method[J]. Advances in Aeronautical Science and Engineering, 2022, 13(6): 1–16. doi: 10.16615/j.cnki.1674-8190.2022.06.01
[73]	张野平, 侯银珠, 汪发亮. 飞行器绕流介质阻挡放电等离子体流动控制技术综述[J]. 航空科学技术, 2016, 27(6): 5–10. ZHANG Y P, HOU Y Z, WANG F L. Brief introduction of DBD plasma flow control in aircraft design[J]. Aeronautical Science & Technology, 2016, 27(6): 5–10.
[74]	LI G Q, YI S H. Large eddy simulation of dynamic stall flow control for wind turbine airfoil using plasma actuator[J]. Energy, 2020, 212: 118753. doi: 10.1016/j.energy.2020.118753
[75]	LI G Q, ZHANG W G, JIANG Y B. Experimental investigation of dynamic stall flow control for wind turbine airfoils using a plasma actuator[J]. Energy, 2019, 185: 90–101. doi: 10.1016/j.energy.2019.07.017
[76]	ZHANG X, CUI Y D, LI H X. Acoustic streaming flow generated by surface dielectric barrier discharge in quiescent air[J]. Physics of Fluids, 2021, 33(5): 057117. doi: 10.1063/5.0049420
[77]	李国强, 常智强, 张鑫, 等. 翼型动态失速等离子体流动控制试验[J]. 航空学报, 2018, 39(8): 123–135. doi: 10.7527/S1000-6893.2018.22111 LI G Q, CHANG Z Q, ZHANG X, et al. Experiment on flow control of airfoil dynamic stall using plasma actuator[J]. Acta Aeronautica et Astronautica Sinica, 2018, 39(8): 123–135. doi: 10.7527/S1000-6893.2018.22111
[78]	MANOJ KUMAR V, WANG C C. Active flow control of flapping airfoil using openfoam[J]. Journal of Mechanics, 2020, 36(3): 361–372. doi: 10.1017/jmech.2019.46
[79]	CLIFFORD C J, SINGHAL A, SAMIMY M. A study of physics and control of a flow over an airfoil in fully-reverse condition[C]//Proc of the 52nd Aerospace Sciences Meeting. 2014: 1265. doi: 10.2514/6.2014-1265
[80]	SOSA R, MOREAU E, TOUCHARD G, et al. Stall control at high angle of attack with periodically excited EHD actuators[C]//Proc of the 35th AIAA Plasmadynamics and Lasers Conference. 2004: 2738. doi: 10.2514/6.2004-2738
[81]	POST M L, CORKE T C. Separation control using plasma actuators: dynamic stall vortex control on oscillating airfoil[J]. AIAA Journal, 2006, 44(12): 3125–3135. doi: 10.2514/1.22716
[82]	YANG H S, LIANG H, ZHAO G Y, et al. Experimental study on dynamic stall control based on AC-DBD actuation[J]. Plasma Science and Technology, 2021, 23(11): 115502. doi: 10.1088/2058-6272/ac1395
[83]	YANG H S, ZHAO G Y, LIANG H, et al. Dynamic stall control over an airfoil by NS-DBD actuation[J]. Chinese Physics B, 2020, 29(10): 105203. doi: 10.1088/1674-1056/abb227
[84]	YU H C, ZHENG J G. Numerical investigation of control of dynamic stall over a NACA0015 airfoil using dielectric barrier discharge plasma actuators[J]. Physics of Fluids, 2020, 32(3): 035103. doi: 10.1063/1.5142465
[85]	POST M L, CORKE T C. Separation control on High angle of attack airfoil using plasma actuators[J]. AIAA Journal, 2004, 42(11): 2177–2184. doi: 10.2514/1.2929
[86]	GLEZER A, AMITAY M. Synthetic jets[J]. Annual Review of Fluid Mechanics, 2002, 34: 503–529. doi: 10.1146/annurev.fluid.34.090501.094913
[87]	罗振兵, 夏智勋. 合成射流技术及其在流动控制中应用的进展[J]. 力学进展, 2005, 35(2): 221–234. doi: 10.3321/j.issn:1000-0992.2005.02.009 LUO Z B, XIA Z X. Advances in synthetic jet technology and applications in flow control[J]. Advances in Mechanics, 2005, 35(2): 221–234. doi: 10.3321/j.issn:1000-0992.2005.02.009
[88]	LIU R B, WEI W T, WAN H P, et al. Experimental study on airfoil flow separation control via an air-supplement plasma synthetic jet[J]. Advances in Aerodynamics, 2022, 4(1): 1–22. doi: 10.1186/s42774-022-00126-w
[89]	李斌斌, 姚勇, 顾蕴松, 等. 合成射流低速射流矢量偏转控制的PIV实验研究[J]. 空气动力学学报, 2018, 36(1): 22–25,30. doi: 10.7638/kqdlxxb-2015.0194 LI B B, YAO Y, GU Y S, et al. PIV experiments on vector deflection control of lowspeed synthetic jet[J]. Acta Aerodynamica Sinica, 2018, 36(1): 22–25,30. doi: 10.7638/kqdlxxb-2015.0194
[90]	罗振兵, 夏智勋, 邓雄, 等. 合成双射流及其流动控制技术研究进展[J]. 空气动力学学报, 2017, 35(2): 252–264. doi: 10.7638/kqdlxxb-2017.0053 LUO Z B, XIA Z X, DENG X, et al. Research progress of dual synthetic jets and its flow control technology[J]. Acta Aerodynamica Sinica, 2017, 35(2): 252–264. doi: 10.7638/kqdlxxb-2017.0053
[91]	左伟, 顾蕴松, 程克明, 等. 斜出口合成射流控制机翼分离流实验研究[J]. 实验流体力学, 2014, 28(6): 45–50. ZUO W, GU Y S, CHENG K M, et al. An experimental investigation on separation control of an airfoil by beveled-slit-synthetic-j et-actuator[J]. Journal of Experiments in Fluid Mechanics, 2014, 28(6): 45–50.
[92]	FENG J J, ZHU G J, LIN Y, et al. Control of dynamic stall of an airfoil by using synthetic jet technology[J]. Arabian Journal for Science and Engineering, 2020, 45(11): 9835–9841. doi: 10.1007/s13369-020-04954-0
[93]	ZHAO Q J, MA Y Y, ZHAO G Q. Parametric analyses on dynamic stall control of rotor airfoil via synthetic jet[J]. Chinese Journal of Aeronautics, 2017, 30(6): 1818–1834. doi: 10.1016/j.cja.2017.08.011
[94]	AMITAY M, SMITH D R, KIBENS V, et al. Aerodynamic flow control over an unconventional airfoil using synthetic jet actuators[J]. AIAA Journal, 2001, 39(3): 361–370. doi: 10.2514/2.1323
[95]	TOUSI N M, COMA M, BERGADÀ J M, et al. Active flow control optimisation on SD7003 airfoil at pre and post-stall angles of attack using synthetic jets[J]. Applied Mathematical Modelling, 2021, 98: 435–464. doi: 10.1016/j.apm.2021.05.016
[96]	MA Y Y, ZHAO Q J, CHEN X, et al. Experimental analyses of synthetic jet control effects on aerodynamic characteristics of helicopter rotor[J]. The Aeronautical Journal, 2020, 124(1274): 597–616. doi: 10.1017/aer.2019.163
[97]	ZHAO G Q, ZHAO Q J. Parametric analyses for synthetic jet control on separation and stall over rotor airfoil[J]. Chinese Journal of Aeronautics, 2014, 27(5): 1051–1061. doi: 10.1016/j.cja.2014.03.023
[98]	DUVIGNEAU R, HAY A, VISONNEAU M. Optimal location of a synthetic jet on an airfoil for stall control[J]. Journal of Fluids Engineering, 2007, 129(7): 825–833. doi: 10.1115/1.2742729
[99]	史勇杰, 厉聪聪, 徐国华. 基于合成射流的旋翼翼型动态失速控制研究[J]. 南京航空航天大学学报, 2020, 52(2): 270–279. doi: 10.16356/j.1005-2615.2020.02.013 SHI Y J, LI C C, XU G H. Rotor airfoil dynamic stall control based on synthetic jet[J]. Journal of Nanjing University of Aeronautics & Astronautics, 2020, 52(2): 270–279. doi: 10.16356/j.1005-2615.2020.02.013
[100]	胡智. 翼型失速特性与合成射流流动控制研究[D]. 上海: 上海交通大学, 2017: 57. HU Z. Study on stall characteristics of airfoil and flow control of synthetic jet[D]. Shanghai: Shanghai Jiao Tong University, 2017: 57.
[101]	KIM J, PARK Y M, LEE J, et al. Numerical investigation of jet angle effect on airfoil stall control[J]. Applied Sciences, 2019, 9(15): 2960. doi: 10.3390/app9152960
[102]	林彦良, 刘艳明, 李智慧. 不同孔口构型合成射流激励器的低速翼型分离控制特性[J]. 中国科技论文, 2013, 8(11): 1173–1178. doi: 10.3969/j.issn.2095-2783.2013.11.022 LIN Y L, LIU Y M, LI Z H. Separation control characteristics of different configurations of orifice synthetic jet actuators used in low-speed airfoil[J]. Sciencepaper Online, 2013, 8(11): 1173–1178. doi: 10.3969/j.issn.2095-2783.2013.11.022
[103]	LEE B, KIM M, CHOI B, et al. Closed-loop active flow control of stall separation using synthetic jets[C]//Proc of the 31st AIAA Applied Aerodynamics Conference. 2013: 2925. doi: 10.2514/6.2013-2925
[104]	罗振兵. 合成射流/合成双射流机理及其在射流矢量控制和微泵中的应用研究[D]. 长沙: 国防科学技术大学, 2006: 176-177. LUO Z B. Principle of synthetic jet and dual synthetic jets, and their applications in jet vectoring and micro-pump[D]. Changsha: National University of Defense Technology, 2006: 176-177.
[105]	WANG P L, LIU Q S, LI C, et al. Effect of trailing edge dual synthesis jets actuator on aerodynamic characteristics of a straight-bladed vertical axis wind turbine[J]. Energy, 2022, 238: 121792. doi: 10.1016/j.energy.2021.121792
[106]	戴昱, 陈德龙, 信志强. 基于流固耦合的柔性翼型动态失速特性研究[J]. 河南科学, 2022, 40(1): 25–32. DAI Y, CHEN D L, XIN Z Q. Study on dynamic stall characteristics of the flexible airfoil based on fluid-structure interaction[J]. Henan Science, 2022, 40(1): 25–32.
[107]	JACOBELLIS G, GANDHI F, RICE T T, et al. Computational and experimental investigation of camber-morphing airfoils for reverse flow drag reduction on high-speed rotorcraft[J]. Journal of the American Helicopter Society, 2020, 65(1): 1–14. doi: 10.4050/jahs.65.012001
[108]	RICE T T, KO D, AMITAY M. Control of reversed flow in static and dynamic conditions using camber morphing airfoils[C]//Proc of the AIAA Aviation 2019 Forum. 2019: 3213. doi: 10.2514/6.2019-3213
[109]	欧阳炎, 寇西平, 郭洪涛, 等. 带连续变弯度后缘操纵面机翼的动态失速减缓[J]. 航空工程进展, 2021, 12(6): 39–49. doi: 10.16615/j.cnki.1674-8190.2021.06.04 OUYANG Y, KOU X P, GUO H T, et al. Alleviation of dynamic stall moments by morphing flap[J]. Advances in Aeronautical Science and Engineering, 2021, 12(6): 39–49. doi: 10.16615/j.cnki.1674-8190.2021.06.04
[110]	KO D, GUHA T K, AMITAY M. Control of reverse flow over a cantilevered blade using passive camber morphing[J]. AIAA Journal, 2021, 59(12): 5310–5331. doi: 10.2514/1.j060229
[111]	NELSON C, GUHA T K, AMITAY M. Control of reverse flow over a cantilevered swept blade using passive camber morphing[C]//Proc of the AIAA SCITECH 2022 Forum. 2022. doi: 10.2514/6.2022-0475
[112]	MA Y Y, ZHAO Q J, ZHAO G Q. New combinational active control strategy for improving aerodynamic characteristics of airfoil and rotor[J]. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2020, 234(4): 977–996. doi: 10.1177/0954410019893193
[113]	DAI X Y, QIU Z, LI G H, et al. Research on dynamic stall active control of two-dimensional airfoil with combination of droop leading edge and trailing edge flap[J]. Aerospace Systems, 2022, 5(4): 643–653. doi: 10.1007/s42401-022-00159-5
[114]	PATERAS P R. Screw propeller of helicopter flying machines: US1449129[P/OL]. 1923-03-20[2023-04-13]. https://www.freepatentsonline.com/1449129.pdf.
[115]	陆洋. 电控旋翼—一种新概念旋翼系统[J]. 航空科学技术, 2007, 18(6): 12–16. doi: 10.3969/j.issn.1007-5453.2007.06.003 LU Y. Electrically controlled rotor—a new concept rotor system[J]. Aeronautical Science and Technology, 2007, 18(6): 12–16. doi: 10.3969/j.issn.1007-5453.2007.06.003
[116]	HALL S R, ANAND R V, STRAUB F K, et al. Active flap control of the SMART rotor for vibration reduction[C]//Proc of the American Helicopter Society 65th annual forum and technology display. 2009.
[117]	KRZYSIAK A, NARKIEWICZ J. Aerodynamic loads on airfoil with trailing-edge flap pitching with different frequencies[J]. Journal of Aircraft, 2006, 43(2): 407–418. doi: 10.2514/1.15597
[118]	GERONTAKOS P, LEE T. Trailing-edge flap control of dynamic pitching moment[J]. AIAA Journal, 2007, 45(7): 1688–1694. doi: 10.2514/1.27577
[119]	LEE T, SU Y Y. Unsteady airfoil with a harmonically deflected trailing-edge flap[J]. Journal of Fluids and Structures, 2011, 27(8): 1411–1424. doi: 10.1016/j.jfluidstructs.2011.06.008
[120]	王进, 杨茂, 陈凤明. 带后缘襟翼翼型的非定常气动特性数值仿真[J]. 计算机仿真, 2011, 28(2): 88–92. doi: 10.3969/j.issn.1006-9348.2011.02.022 WANG J, YANG M, CHEN F M. CFD simulation of unsteady aerodynamics of airfoil with trailing-edge flap[J]. Computer Simulation, 2011, 28(2): 88–92. doi: 10.3969/j.issn.1006-9348.2011.02.022
[121]	马奕扬, 招启军, 赵国庆. 基于后缘小翼的旋翼翼型动态失速控制分析[J]. 航空学报, 2017, 38(3): 127–137. doi: 10.7527/S1000-6893.2016.0220 MA Y Y, ZHAO Q J, ZHAO G Q. Dynamic stall control of rotor airfoil via trailing-edge flap[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(3): 127–137. doi: 10.7527/S1000-6893.2016.0220
[122]	马奕扬, 招启军. 后缘小翼对旋翼气动特性的控制机理及参数分析[J]. 航空学报, 2018, 39(5): 14–27. doi: 10.7527/S1000-6893.2018.21671 MA Y Y, ZHAO Q J. Control mechanism and parameter analyses of aerodynamic characteristics of rotor via trailing-edge flap[J]. Acta Aeronautica et Astronautica Sinica, 2018, 39(5): 14–27. doi: 10.7527/S1000-6893.2018.21671
[123]	胡志远, 徐国华, 史勇杰. 基于CFD方法的主动襟翼控制旋翼翼型涡特性研究[J]. 南京航空航天大学学报, 2018, 50(2): 167–172. doi: 10.16356/j.1005-2615.2018.02.003 HU Z Y, XU G H, SHI Y J. Study of AFC rotor airfoil vortex characteristics based on CFD method[J]. Journal of Nanjing University of Aeronautics & Astronautics, 2018, 50(2): 167–172. doi: 10.16356/j.1005-2615.2018.02.003
[124]	BARRIO J F, MERTENS C, RAGNI D, et al. Pressure based active load control of a blade in dynamic stall conditions[J]. Journal of Physics: Conference Series, 2020, 1618(2): 022003. doi: 10.1088/1742-6596/1618/2/022003
[125]	SAMARA F, JOHNSON D A. Deep dynamic stall and active aerodynamic modification on a S833 airfoil using pitching trailing edge flap[J]. Wind Engineering, 2020, 00(0): 1–20. doi: 10.1177/0309524X209388
[126]	刘洋, 向锦武. 后缘襟翼对直升机旋翼翼型动态失速特性的影响[J]. 航空学报, 2013, 34(5): 1028–1035. doi: 10.7527/S1000-6893.2013.0112 LIU Y, XIANG J W. Effect of the trailing edge flap on dynamic stall performance of helicopter rotor airfoil[J]. Acta Aeronautica et Astronautica Sinica, 2013, 34(5): 1028–1035. doi: 10.7527/S1000-6893.2013.0112
[127]	KAN Z, LI D C, XIANG J W, et al. Delaying stall of morphing wing by periodic trailing-edge deflection[J]. Chinese Journal of Aeronautics, 2020, 33(2): 493–500. doi: 10.1016/j.cja.2019.09.028
[128]	WOODS B K S, FRISWELL M I. Preliminary investigation of a fishbone active camber concept[C]//Proceedings of ASME 2012 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. 2013: 555-563. doi: 10.1115/SMASIS2012-8058
[129]	KUMAR S, KOMP D, HAJEK M, et al. Integrated rotor performance improvement and vibration reduction using active camber morphing[C]//ASME 2019 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. 2019. doi: 10.1115/SMASIS2019-5588
[130]	RIVERO A E, FOURNIER S, MANOLESOS M, et al. Experimental aerodynamic comparison of active camber morphing and trailing-edge flaps[J]. AIAA Journal, 2021, 59(7): 2627–2640. doi: 10.2514/1.j059606
[131]	POHL J E, RADESPIEL R, HERRMANN B, et al. Gust mitigation through closed-loop control. I. Trailing-edge flap response[J]. Physical Review Fluids, 2022, 7(2): 024705. doi: 10.1103/physrevfluids.7.024705