基于联合射流的翼型动态失速流动控制研究
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摘要
动态失速控制对于提高翼型气动特性具有重要意义。采用联合射流方法对翼型俯仰动态失速控制进行数值模拟,完成两方面的研究:一是射流关闭时射流通道对动态失速特性的影响,二是射流开启时不同射流动量系数对动态失速控制的影响和分析。结果表明:射流关闭时,射流通道的存在对翼型上仰过程中附着流阶段的气动特性产生不利影响,使得升力系数明显下降,但是对翼型下俯过程中失速分离流阶段的气动特性影响不明显;射流开启后,动态失速特性得到极大改善,迟滞环面积显著减小,升力增加,阻力减小,且阻力和力矩的峰值显著减小,原基准翼型力矩曲线的负阻尼区域消失。
Dynamic stall control is of great significance for enhancement of the airfoil aerodynamic characteristics.In the present study,the co-flow jet(CFJ)flow control method is numerically investigated to control the dynamic stall caused by the pitching airfoil.Two aspects regarding the CFJ implementation are studied:one is the effect of the CFJ channel on the dynamic stall characteristics when the jet is switched off and another is the effect of jet momentum coefficient on the dynamic stall control effectiveness when the CFJ is activated.Results show that the jet channel will significantly affect the aerodynamic characteristics in the attached flow regime during pitching up,but not have obvious influence on the aerodynamic characteristics in the massively separating regime during the pitching down process.When the jet is activated,the dynamic stall characteristics is significantly improved.The areas of the hysteresis lines are significantly reduced,and the lift is significantly increased,and drag is reduced.The peaks of the drag and moment are significantly reduced.Moreover,the negative damping existing in the moment coefficient hysteresis line of the baseline airfoil is removed,leading to a completely positive damping during the entire pitching cycle.
Dynamic stall control is of great significance for enhancement of the airfoil aerodynamic characteristics.In the present study,the co-flow jet(CFJ)flow control method is numerically investigated to control the dynamic stall caused by the pitching airfoil.Two aspects regarding the CFJ implementation are studied:one is the effect of the CFJ channel on the dynamic stall characteristics when the jet is switched off and another is the effect of jet momentum coefficient on the dynamic stall control effectiveness when the CFJ is activated.Results show that the jet channel will significantly affect the aerodynamic characteristics in the attached flow regime during pitching up,but not have obvious influence on the aerodynamic characteristics in the massively separating regime during the pitching down process.When the jet is activated,the dynamic stall characteristics is significantly improved.The areas of the hysteresis lines are significantly reduced,and the lift is significantly increased,and drag is reduced.The peaks of the drag and moment are significantly reduced.Moreover,the negative damping existing in the moment coefficient hysteresis line of the baseline airfoil is removed,leading to a completely positive damping during the entire pitching cycle.
引文
[1] Martin P B,Wilson J S,Berry J D,et al.Passive control of compressible dynamic stall[R].AIAA-2008-7506,2008.
[2] Heine B,Mulleners K,Joubert G,et al.Dynamic stall control by passive disturbance generators[R].AIAA-2011-3371,2011.
[3] Joo W,Lee B,Yee K,et al.Combining passive control method for dynamic stall control[J].Journal of Aircraft,2006,43(4):1120-1128.
[4]王元元,张彬乾.Gurney襟翼改善翼型动态失速特性研究[J].飞行力学,2010,28(4):5-8.Wang Yuanyuan,Zhang Binqian.Investigation of Gurney flap on improving dynamic stall aerodynamic characteristics of an airfoil[J].Flight Dynamics,2010,28(4):5-8.(in Chinese)
[5] Carr L W,Chandrasekhara M S,Wilder M C,et al.Effect of compressibility on suppression of dynamic stall using a slotted airfoil[J].Journal of Aircraft,2001,38(2):296-309.
[6]张仕栋.波状前缘翼动态失速控制数值研究[D].上海:上海交通大学,2015.Zhang Shidong.Numerical study of dynamic stall control via wavy leading-edge modification[D].Shanghai:Shanghai Jiao Tong University,2015.(in Chinese)
[7] Feszty D,Gillies E A,Vezza M.Alleviation of airfoil dynamic stall moments via trailing-edge-flap flow control[J].AIAA Journal,2004,42(1):17-25.
[8] Gerontakos P,Lee T.Dynamic stall flow control via a trailing-edge flap[J].AIAA Journal,2006,44(3):469-480.
[9]王荣,夏品奇.多片后缘小翼对直升机旋翼桨叶动态失速及桨毂振动载荷的控制[J].航空学报,2013,34(5):1083-1091.Wang Rong,Xia Pinqi.Control of helicopter rotor blade dynamic stall and hub vibration loads by multiple trailing edge flaps[J].Acta Aeronautica et Astronautica Sinica,2013,34(5):1083-1091.(in Chinese)
[10]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.Liu Yang,Xiang Jinwu.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.(in Chinese)
[11]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.Ma Yiyang,Zhao Qijun,Zhao Guoqing.Dynamic stall control of rotor airfoil via trailing-edge flap[J].Acta Aeronautica et Astronautica Sinica,2017,38(3):127-137.(in Chinese)
[12]王建涛.直升机旋翼前缘下垂控制动态失速数值模拟研究[D].绵阳:中国空气动力研究与发展中心,2008.Wang Jiantao.Numerical simulation of dynamic stall control on helicopter rotor wings with variable droop leading edge method[D].Mianyang:China Aerodynamics Research and Development Center,2008.(in Chinese)
[13]黄勇,牟斌,陈作斌,等.翼型动态失速的变下垂前缘控制数值模拟[J].航空动力学报,2008,23(3):496-504.Huang Yong,Mou Bin,Chen Zuobin,et al.Numerical investigation of dynamic stall control using variable droop leading edge airfoil[J].Journal of Aerospace Power,2008,23(3):496-504.(in Chinese)
[14] Zhao G Q,Zhao Q J.Dynamic stall control optimization of rotor airfoil via variable droop leading-edge[J].Aerospace Science and Technology,2015,43:406-414.
[15] Geisslera W,Wall B G.Dynamic stall control on flapping wing airfoils[J].Aerospace Science and Technology,2017,62:1-10.
[16] Niu J,Lei J,Lu T.Numerical research on the effect of variable droop leading-edge on oscillating NACA 0012airfoil dynamic stall[J].Aerospace Science and Technology,2018,72:476-485.
[17] Chandrasekhara M S,Wilder M C,Carr L W.Unsteady stall control using dynamically deforming airfoils[J].AIAA Journal,1998,36(10):1792-1800.
[18] Sahin M,Sankar L M,Chandrasekhara M S,et al.Dynamic stall alleviation using a deformable leading edge concept-a numerical study[J].Journal of Aircraft,2003,40(1):77-85.
[19]葛兰.波动翼对动态失速控制的研究[D].上海:上海交通大学,2013.Ge Lan.Study on dynamic stall control of undulatory airfoils[D].Shanghai:Shanghai Jiao Tong University,2013.(in Chinese)
[20]许和勇,邢世龙,叶正寅,等.基于充气前缘技术的旋翼翼型动态失速抑制[J].航空学报,2017,38(6):91-103.Xu Heyong,Xing Shilong,Ye Zhengyin,et al.Dynamic stall suppression for rotor airfoil based on inflatable leading edge technology[J].Acta Aeronautica et Astronautica Sinica,2017,38(6):91-103.(in Chinese)
[21] Wang Q,Zhao Q J.Rotor airfoil profile optimization for alleviating dynamic stall characteristics[J].Aerospace Science and Technology,2018,72:502-515.
[22] Singh C,Peake D J,Kokkalis A,et al.A control of rotorcraft retreating blade stall using air-jet vortex generators[J].Journal of Aircraft,2006,43(4):1169-1176.
[23] Ekaterinaris J A.Numerical investigations of dynamic stall active control for incompressible and compressible flows[J].Journal of Aircraft,2002,39(1):71-78.
[24] Muller-Vahl H F,Strangfeld C,Nayeri C N,et al.Control of thick airfoil deep dynamic stall using steady blowing[J].AIAA Journal,2015,53(2):277-295.
[25] Traub L W,Miller A,Rediniotis O.Effects of synthetic jet actuation on a ramping NACA 0015airfoil[J].Journal of Aircraft,2004,41(5):1153-1162.
[26] Florea R,Wake B E.Parametric analysis of directed-synthetic jets for improved dynamic-stall performance[R].AIAA-2003-0216,2003.
[27]蒋瑾,杨爱明,翁培奋.合成射流用于动态失速控制的数值模拟[J].上海大学学报:自然科学版,2008,14(4):405-411.Jiang Jin, Yang Aiming, Weng Peifen. Numerical simulation of dynamic stall control using synthetic jet[J].Journal of Shanghai University:Natural Science,2008,14(4):405-411.(in Chinese)
[28]韩忠华,宋文萍,乔志德.OA212翼型主动流动控制的数值模拟研究[J].空气动力学学报,2009,27(6):639-644.Han Zhonghua,Song Wenping,Qiao Zhide.Numerical simulation of active dynamic stall control on an OA212rotor airfoil[J].Acta Aerodynamica Sinica,2009,27(6):639-644.(in Chinese)
[29] 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.
[30]宋科,杨旭东,乔志德.翼型动态失速DBD等离子体流动控制的数值模拟研究[J].航空计算技术,2010,40(3):5-8,17.Song Ke,Yang Xudong,Qiao Zhide.Flow control of airfoil dynamic stall based on DBD plasma actuators[J].Aeronautical Computing Technique,2010,40(3):5-8,17.(in Chinese)
[31] Corke T C,Bowles P O,He C,et al.Sensing and control of flow separation using plasma actuators[J].Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences,2011,369:1459-1475.
[32] Lombardi A J,Bowles P O,Corke T C.Closed-loop dynamic stall control using aplasma actuator[J].AIAA Journal,2013,51:1130-1141.
[33] Zha G C,Paxton C.A novel airfoil circulation augment flow control method using co-flow jet[R]. AIAA-2004-2208,2004.
[34] Zha G C,Carroll B F,Paxton C D,et al.High-performance airfoil using co-flow jet flow control[J].AIAA Journal,2007,45(8):2087-2090.
[35] Wang B,Haddoukessouni B,Levy J,et al.Numerical investigations of injection-slot-size effect on the performance of coflow jet airfoils[J].Journal of Aircraft,2008,45(6):2084-2091.
[36] Lefebvre A,Zha G C.Numerical simulation of pitching airfoil performance enhancement using co-flow jet flow control[R].AIAA-2013-2517,2013.
[37]刘沛清,旷建敏,屈秋林.联合射流控制技术的增升效果和机理[J].北京航空航天大学学报,2009,35(6):737-740.Liu Peiqing,Kuang Jianmin,Qu Qiulin.Effect and mechanism of lift enhancement of the co-flow jet technology[J].Journal of Beijing University of Aeronautics and Astronautics,2009,35(6):737-740.(in Chinese)
[38]朱敏,杨旭东,宋超,等.应用协同射流控制的临近空间螺旋桨高增效方法[J].航空学报,2014,35(6):1549-1559.Zhu Min,Yang Xudong,Song Chao,et al.High synergy method for near space propeller using co-flow jet control[J].Acta Aeronautica et Astronautica Sinica,2014,35(6):1549-1559.(in Chinese)
[39] Xu H Y,Xing S L,Ye Z Y.Numerical study of the S809airfoil aerodynamic performance using a co-flow jet active control concept[J].Journal of Renewable and Sustainable Energy,2015,7(2):033127-226.
[40] Spalart P,Allmaras S.A one-equation turbulence model for aerodynamic flows[R].AIAA-92-0439,1992.
[41] Jamson A,Schmidt W,Turkel E.Numerical solutions of the Euler equations by finite volume methods using RungeKutta time stepping scheme[R].AIAA-81-1259,1981.
[42] Roe P.Approximate riemann solvers parameter vectors,and difference schemes[J].Journal of Computational Physics,1981,43:357-372.
[43] Leer B.Towards the ultimate conservative difference scheme a second order sequel to Godunov’s method[J].Journal of Computational Physics,1979,32:101-136.
[44] Jameson A.Time dependent calculations using multi-grid with applications to unsteady flows past airfoil and wings[R].AIAA-91-1596,1991.
[45] Yoon S,Jameson A.Lower-upper symmetric-gauss-seidel method for the Euler and Navier-Stokes equations[J].AIAA Journal,1988,26:1025-1026.
[46] Hermanns M.Parallel programming in fortran 95using OpenMP[R].Spain:Universidad Politecnica De Madrid,2002.
[47] Jameson A,Baker T.Multigrid solution of the Euler equations for aircraft configurations[R].AIAA-84-0093,1984.
[48] McAlister K W,Pucci S L,McCroskey W J,et al.An experimental study of dynamic stall on advanced airfoil sections,Volume 2:pressure and force data[R].NASA-TM-84245,1982.
[49]陈文轩.直升机动态失速研究[J].直升机技术,2008(3):4-18.Chen Wenxuan.Helicopter dynamic stall study[J].Helicopter Technique,2008(3):4-18.(in Chinese)
[50]俞国华,竺晓程,杜朝辉.俯仰风力机翼型动态失速数值模拟[J].太阳能学报,2011,32(11):1571-1579.Yu Guohua,Zhu Xiaocheng,Du Zhaohui.Numerical simulation of pitching wind turbine airfoil dynamic stall[J].Acta Energiae Solaris Sinica,2011,32(11):1571-1579.(in Chinese)
[2] Heine B,Mulleners K,Joubert G,et al.Dynamic stall control by passive disturbance generators[R].AIAA-2011-3371,2011.
[3] Joo W,Lee B,Yee K,et al.Combining passive control method for dynamic stall control[J].Journal of Aircraft,2006,43(4):1120-1128.
[4]王元元,张彬乾.Gurney襟翼改善翼型动态失速特性研究[J].飞行力学,2010,28(4):5-8.Wang Yuanyuan,Zhang Binqian.Investigation of Gurney flap on improving dynamic stall aerodynamic characteristics of an airfoil[J].Flight Dynamics,2010,28(4):5-8.(in Chinese)
[5] Carr L W,Chandrasekhara M S,Wilder M C,et al.Effect of compressibility on suppression of dynamic stall using a slotted airfoil[J].Journal of Aircraft,2001,38(2):296-309.
[6]张仕栋.波状前缘翼动态失速控制数值研究[D].上海:上海交通大学,2015.Zhang Shidong.Numerical study of dynamic stall control via wavy leading-edge modification[D].Shanghai:Shanghai Jiao Tong University,2015.(in Chinese)
[7] Feszty D,Gillies E A,Vezza M.Alleviation of airfoil dynamic stall moments via trailing-edge-flap flow control[J].AIAA Journal,2004,42(1):17-25.
[8] Gerontakos P,Lee T.Dynamic stall flow control via a trailing-edge flap[J].AIAA Journal,2006,44(3):469-480.
[9]王荣,夏品奇.多片后缘小翼对直升机旋翼桨叶动态失速及桨毂振动载荷的控制[J].航空学报,2013,34(5):1083-1091.Wang Rong,Xia Pinqi.Control of helicopter rotor blade dynamic stall and hub vibration loads by multiple trailing edge flaps[J].Acta Aeronautica et Astronautica Sinica,2013,34(5):1083-1091.(in Chinese)
[10]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.Liu Yang,Xiang Jinwu.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.(in Chinese)
[11]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.Ma Yiyang,Zhao Qijun,Zhao Guoqing.Dynamic stall control of rotor airfoil via trailing-edge flap[J].Acta Aeronautica et Astronautica Sinica,2017,38(3):127-137.(in Chinese)
[12]王建涛.直升机旋翼前缘下垂控制动态失速数值模拟研究[D].绵阳:中国空气动力研究与发展中心,2008.Wang Jiantao.Numerical simulation of dynamic stall control on helicopter rotor wings with variable droop leading edge method[D].Mianyang:China Aerodynamics Research and Development Center,2008.(in Chinese)
[13]黄勇,牟斌,陈作斌,等.翼型动态失速的变下垂前缘控制数值模拟[J].航空动力学报,2008,23(3):496-504.Huang Yong,Mou Bin,Chen Zuobin,et al.Numerical investigation of dynamic stall control using variable droop leading edge airfoil[J].Journal of Aerospace Power,2008,23(3):496-504.(in Chinese)
[14] Zhao G Q,Zhao Q J.Dynamic stall control optimization of rotor airfoil via variable droop leading-edge[J].Aerospace Science and Technology,2015,43:406-414.
[15] Geisslera W,Wall B G.Dynamic stall control on flapping wing airfoils[J].Aerospace Science and Technology,2017,62:1-10.
[16] Niu J,Lei J,Lu T.Numerical research on the effect of variable droop leading-edge on oscillating NACA 0012airfoil dynamic stall[J].Aerospace Science and Technology,2018,72:476-485.
[17] Chandrasekhara M S,Wilder M C,Carr L W.Unsteady stall control using dynamically deforming airfoils[J].AIAA Journal,1998,36(10):1792-1800.
[18] Sahin M,Sankar L M,Chandrasekhara M S,et al.Dynamic stall alleviation using a deformable leading edge concept-a numerical study[J].Journal of Aircraft,2003,40(1):77-85.
[19]葛兰.波动翼对动态失速控制的研究[D].上海:上海交通大学,2013.Ge Lan.Study on dynamic stall control of undulatory airfoils[D].Shanghai:Shanghai Jiao Tong University,2013.(in Chinese)
[20]许和勇,邢世龙,叶正寅,等.基于充气前缘技术的旋翼翼型动态失速抑制[J].航空学报,2017,38(6):91-103.Xu Heyong,Xing Shilong,Ye Zhengyin,et al.Dynamic stall suppression for rotor airfoil based on inflatable leading edge technology[J].Acta Aeronautica et Astronautica Sinica,2017,38(6):91-103.(in Chinese)
[21] Wang Q,Zhao Q J.Rotor airfoil profile optimization for alleviating dynamic stall characteristics[J].Aerospace Science and Technology,2018,72:502-515.
[22] Singh C,Peake D J,Kokkalis A,et al.A control of rotorcraft retreating blade stall using air-jet vortex generators[J].Journal of Aircraft,2006,43(4):1169-1176.
[23] Ekaterinaris J A.Numerical investigations of dynamic stall active control for incompressible and compressible flows[J].Journal of Aircraft,2002,39(1):71-78.
[24] Muller-Vahl H F,Strangfeld C,Nayeri C N,et al.Control of thick airfoil deep dynamic stall using steady blowing[J].AIAA Journal,2015,53(2):277-295.
[25] Traub L W,Miller A,Rediniotis O.Effects of synthetic jet actuation on a ramping NACA 0015airfoil[J].Journal of Aircraft,2004,41(5):1153-1162.
[26] Florea R,Wake B E.Parametric analysis of directed-synthetic jets for improved dynamic-stall performance[R].AIAA-2003-0216,2003.
[27]蒋瑾,杨爱明,翁培奋.合成射流用于动态失速控制的数值模拟[J].上海大学学报:自然科学版,2008,14(4):405-411.Jiang Jin, Yang Aiming, Weng Peifen. Numerical simulation of dynamic stall control using synthetic jet[J].Journal of Shanghai University:Natural Science,2008,14(4):405-411.(in Chinese)
[28]韩忠华,宋文萍,乔志德.OA212翼型主动流动控制的数值模拟研究[J].空气动力学学报,2009,27(6):639-644.Han Zhonghua,Song Wenping,Qiao Zhide.Numerical simulation of active dynamic stall control on an OA212rotor airfoil[J].Acta Aerodynamica Sinica,2009,27(6):639-644.(in Chinese)
[29] 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.
[30]宋科,杨旭东,乔志德.翼型动态失速DBD等离子体流动控制的数值模拟研究[J].航空计算技术,2010,40(3):5-8,17.Song Ke,Yang Xudong,Qiao Zhide.Flow control of airfoil dynamic stall based on DBD plasma actuators[J].Aeronautical Computing Technique,2010,40(3):5-8,17.(in Chinese)
[31] Corke T C,Bowles P O,He C,et al.Sensing and control of flow separation using plasma actuators[J].Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences,2011,369:1459-1475.
[32] Lombardi A J,Bowles P O,Corke T C.Closed-loop dynamic stall control using aplasma actuator[J].AIAA Journal,2013,51:1130-1141.
[33] Zha G C,Paxton C.A novel airfoil circulation augment flow control method using co-flow jet[R]. AIAA-2004-2208,2004.
[34] Zha G C,Carroll B F,Paxton C D,et al.High-performance airfoil using co-flow jet flow control[J].AIAA Journal,2007,45(8):2087-2090.
[35] Wang B,Haddoukessouni B,Levy J,et al.Numerical investigations of injection-slot-size effect on the performance of coflow jet airfoils[J].Journal of Aircraft,2008,45(6):2084-2091.
[36] Lefebvre A,Zha G C.Numerical simulation of pitching airfoil performance enhancement using co-flow jet flow control[R].AIAA-2013-2517,2013.
[37]刘沛清,旷建敏,屈秋林.联合射流控制技术的增升效果和机理[J].北京航空航天大学学报,2009,35(6):737-740.Liu Peiqing,Kuang Jianmin,Qu Qiulin.Effect and mechanism of lift enhancement of the co-flow jet technology[J].Journal of Beijing University of Aeronautics and Astronautics,2009,35(6):737-740.(in Chinese)
[38]朱敏,杨旭东,宋超,等.应用协同射流控制的临近空间螺旋桨高增效方法[J].航空学报,2014,35(6):1549-1559.Zhu Min,Yang Xudong,Song Chao,et al.High synergy method for near space propeller using co-flow jet control[J].Acta Aeronautica et Astronautica Sinica,2014,35(6):1549-1559.(in Chinese)
[39] Xu H Y,Xing S L,Ye Z Y.Numerical study of the S809airfoil aerodynamic performance using a co-flow jet active control concept[J].Journal of Renewable and Sustainable Energy,2015,7(2):033127-226.
[40] Spalart P,Allmaras S.A one-equation turbulence model for aerodynamic flows[R].AIAA-92-0439,1992.
[41] Jamson A,Schmidt W,Turkel E.Numerical solutions of the Euler equations by finite volume methods using RungeKutta time stepping scheme[R].AIAA-81-1259,1981.
[42] Roe P.Approximate riemann solvers parameter vectors,and difference schemes[J].Journal of Computational Physics,1981,43:357-372.
[43] Leer B.Towards the ultimate conservative difference scheme a second order sequel to Godunov’s method[J].Journal of Computational Physics,1979,32:101-136.
[44] Jameson A.Time dependent calculations using multi-grid with applications to unsteady flows past airfoil and wings[R].AIAA-91-1596,1991.
[45] Yoon S,Jameson A.Lower-upper symmetric-gauss-seidel method for the Euler and Navier-Stokes equations[J].AIAA Journal,1988,26:1025-1026.
[46] Hermanns M.Parallel programming in fortran 95using OpenMP[R].Spain:Universidad Politecnica De Madrid,2002.
[47] Jameson A,Baker T.Multigrid solution of the Euler equations for aircraft configurations[R].AIAA-84-0093,1984.
[48] McAlister K W,Pucci S L,McCroskey W J,et al.An experimental study of dynamic stall on advanced airfoil sections,Volume 2:pressure and force data[R].NASA-TM-84245,1982.
[49]陈文轩.直升机动态失速研究[J].直升机技术,2008(3):4-18.Chen Wenxuan.Helicopter dynamic stall study[J].Helicopter Technique,2008(3):4-18.(in Chinese)
[50]俞国华,竺晓程,杜朝辉.俯仰风力机翼型动态失速数值模拟[J].太阳能学报,2011,32(11):1571-1579.Yu Guohua,Zhu Xiaocheng,Du Zhaohui.Numerical simulation of pitching wind turbine airfoil dynamic stall[J].Acta Energiae Solaris Sinica,2011,32(11):1571-1579.(in Chinese)