小振幅振动翼型升力迟滞环变向的成因分析
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摘要
在低雷诺数条件下研究了SD7037翼型小振幅强迫振动时,振动轴位置和减缩频率对翼型气动特性的影响。通过升力系数随时间变化曲线与迎角随时间变化曲线的对比,发现引起升力系数随迎角变化的迟滞环变向的原因主要是升力系数随时间变化曲线的相位发生变化,并从数学上证明了这个相位是关于减缩频率的函数。而且,当升力系数随时间变化曲线的相位变大时,会使得对应的升力系数随迎角变化的迟滞环曲线从逆时针向顺时针方向变化,这中间必然会经历一个"直线"过程,就好像迟滞现象消失了一样。进一步通过对比流场,发现振动轴位置和减缩频率对此相位的影响机制不同,振动轴位置主要改变翼型的有效迎角,而减缩频率的增大则影响了周围流场结构,使得附加质量带来的反作用力变大,进而提高升力,振动轴向前移动和减缩频率的增大都会增大升力系数曲线的相位。
This paper studies the effects of the pivot location and the reduction frequency on the aerodynamic characteristics of the SD7037 airfoil under small amplitude forced oscillation at low Reynolds number.By comparing lift coefficient-time curve with angle of attack-time curve,it is found that the hysteresis loop direction changing of the lift coefficient varies with the angle of attack is mainly due to the change of the phase of the lift coefficient-time curve.It is proved mathematically that the phase is a function of reduction frequency.What's more,when the phase of the lift coefficient-time curve increases,the hysteresis loop of the corresponding lift coefficient-angle of attack curve will change from counterclockwise to clockwise.In this process,the lift coefficient-angle of attack curve inevitably shows a straight line shape,as if the hysteresis phenomenon"disappears".In addition,by comparing the flow field structure,it is found that the pivot location and reduction frequency have different impact on this phase.While the pivot location mainly changes the effective angle of attack of the airfoil,the increase of reduction frequency affects the structure of the surrounding flow field,so that the reaction force brought by the added mass becomes stronger,and thus the lift is improved.Both the forward movement of the pivot location and the increase of reduction frequency will increase the phase of the lift coefficient curve.
This paper studies the effects of the pivot location and the reduction frequency on the aerodynamic characteristics of the SD7037 airfoil under small amplitude forced oscillation at low Reynolds number.By comparing lift coefficient-time curve with angle of attack-time curve,it is found that the hysteresis loop direction changing of the lift coefficient varies with the angle of attack is mainly due to the change of the phase of the lift coefficient-time curve.It is proved mathematically that the phase is a function of reduction frequency.What's more,when the phase of the lift coefficient-time curve increases,the hysteresis loop of the corresponding lift coefficient-angle of attack curve will change from counterclockwise to clockwise.In this process,the lift coefficient-angle of attack curve inevitably shows a straight line shape,as if the hysteresis phenomenon"disappears".In addition,by comparing the flow field structure,it is found that the pivot location and reduction frequency have different impact on this phase.While the pivot location mainly changes the effective angle of attack of the airfoil,the increase of reduction frequency affects the structure of the surrounding flow field,so that the reaction force brought by the added mass becomes stronger,and thus the lift is improved.Both the forward movement of the pivot location and the increase of reduction frequency will increase the phase of the lift coefficient curve.
引文
[1]FLITTIE K,CURTIN B.Pathfinder solar-powered aircraft flight performance:AIAA-1998-4446[R].Reston,VA:AIAA,1998.
[2]NOLL T,BROWN J,PEREZ-DAVIS M,et al.Investigation of the Helios prototype aircraft mishap report:Mishap Report Voume I[R].Washington,D.C.:NASA,2004.
[3]张健,张德虎.高空长航时太阳能无人机总体设计要点分析[J].航空学报,2016,37(S1):1-7.ZHANG J,ZHANG D H.Essentials of configuration design of HALE solar-powered UAVs[J].Acta Aeronautica et Astronautica Sinica,2016,37(S1):1-7(in Chinese).
[4]尹成越,高普云,郭健,等.“微风”(Zephyr7)无人机机翼力学性能分析[J].强度与环境,2012,39(3):19-25.YIN C Y,GAO P Y,GUO J,et al.Mechanical performance analysis on wing’s of Zephyr7UAV[J].Structure&Enviroment Engineering,2012,39(3):19-25(in Chinese).
[5]RAPINETT A.Zephyr:A high altitude long endurance unmanned air vehicle[D].Guildford:University of Surrey,2009:1-8.
[6]ALBERTSON J,TROUTT T,KEDZIE C.Unsteady aerodynamic forces at low airfoil pitching rates:AIAA-1988-2579[R].Reston,VA:AIAA,1988.
[7]HELIN H,WALKER J.Interrelated effects of pitch rate and pivot point on airfoil dynamic stall:AIAA-1985-0130[R].Reston,VA:AIAA,1985.
[8]WALKER J M,HELIN H E,STRICKLAND J H.An experimental investigation of an airfoil undergoing largeamplitude pitching motions[J].AIAA Journal,1985,23(8):1141-1142.
[9]SCHRECK S J,FALLER W E,ROBINSON M C.Unsteady separation processes and leading edge vortex precursors:Pitch rate and Reynolds number influences[J].Journal of Aircraft,2002,39(5):868-875.
[10]OI M V,ELDREDGE J D,WANG C.High-amplitude pitch of a flat plate:An abstraction of perching and flapping[J].International Journal of Micro Air Vehicles,2009,1(3):203-216.
[11]GOPALAKRISHNAN P,TAFTI D K.Effect of rotation kinematics and angle of attack on flapping flight[J].AIAA Journal,2009,47(11):2505-2519.
[12]LEKNYS R R,ARJOMANDI M,KELSO R M,et al.Dynamic-and post-stall characteristics of pitching airfoils at extreme conditions[J].Proceedings of the Institution of Mechanical Engineers,Part G:Journal of Aerospace Engineering,2018,232(6):1171-1185.
[13]高正红.绕振动机翼非定常气动力迟滞特性的模拟研究[J].应用数学和力学,1999,20(8):835-846.GAO Z H.Research on the hysteresis properties of unsteady aerodynamics about the oscillating wings[J].Applied Mathematics and Mechanics,1999,20(8):835-846(in Chinese).
[14]JUNG Y W,PARK S O.Vortex-shedding characteristics in the wake of an oscillating airfoil at low Reynolds number[J].Journal of Fluids and Structures,2005,20(3):451-464.
[15]YU Y,AMANDOLESE X,FAN C,et al.Experimental study and modelling of unsteady aerodynamic forces and moment on flat plate in high amplitude pitch ramp motion[J].Journal of Fluid Mechanics,2018,846:82-120.
[16]QIN S,KOOCHESFAHANI M,JABERI F.Large eddy simulations of unsteady flows over a stationary airfoil[J].Computers&Fluids,2018,161:155-170.
[17]YU H T,BERNAL L P.Effects of pivot location and reduced pitch rate on pitching rectangular flat plates[J].AIAA Journal,2017,55(3):702-718.
[18]EKATERINARIS J A,PLATZER M F.Computational prediction of airfoil dynamic stall[J].Progress in Aerospace Sciences,1998,33(11-12):759-846.
[19]张正秋,邹正平,刘火星,等.非失速二维振荡叶栅非定常流动数值模拟研究[J].空气动力学学报,2009,27(2):255-259.ZHANG Z Q,ZOU Z P,LIU H X,et al.A numericalstudy of unstalled two dimentional flow on an oscillating cascade[J].Acta Aerodynamica Sinica,2009,27(2):255-259(in Chinese).
[20]张正秋,邹正平,刘火星.振荡翼型非定常流动数值模拟研究[J].燃气涡轮试验与研究,2009,22(3):1-8.ZHANG Z Q,ZOU Z P,LIU H X.Numerical study oftwo dimensional flow on an oscillating airfoil[J].Gas Turbine Experiment and Research,2009,22(3):1-8(in Chinese).
[21]MENTER F R.Two-equation eddy-viscosity turbulence models for engineering applications[J].AIAA Journal,1994,32(8):1598-1605.
[22]VISBAL M R.Dynamic stall of a constant-rate pitching airfoil[J].Journal of Aircraft,1990,27(5):400-407.
[23]王科雷,祝小平,周洲,等.基于转捩模型的低雷诺数翼型优化设计研究[J].西北工业大学学报,2015,33(4):580-587.WANG K L,ZHU X P,ZHOU Z,et al.Studying optimization design of low Reynolds number airfoil using transition model[J].Journal of Northwestern Polytechnical University,2015,33(4):580-587(in Chinese).
[24]YANG Z,IGARASHI H,MARTIN M,et al.An experimental investigation on aerodynamic hysteresis of a lowReynolds number airfoil:AIAA-2008-0315[R].Reston,VA:AIAA,2008.
[25]PIZIALI R A.2-D and 3-D oscillating wing aerodynamics for a range of angles of attack including stall:NASA-TM-4632[R].Washington,D.C.:NASA,1994.
[26]MCALISTER K W,PUCCI S L,MCCROSKEY W J,et al.An experimental study of dynamic stall on advanced airfoil section.Volume 2:Pressure and force data:NASA-TM-84245-VOL-2[R].Washington,D.C.:NASA,1982.
[27]THEODORSEN T.General theory of aerodynamic instability and the mechanism of flutter:NACA-TR-496[R].Washington,D.C.:NASA,1949.
[28]叶正寅,张伟伟,史爱明.流固耦合力学基础及其应用[M].哈尔滨:哈尔滨工业大学出版社,2010:73-85.YE Z Y,ZHNAG W W,SHI A M.Fundamentals of fluid-solid coupling mechanics and its application[M].Harbin:Harbin Institute of Technology Press,2010:73-85(in Chinese).
[29]GENDRICH C P,KOOCHESFAHANI M M,VISBALM R.Effects of initial acceleration on the flow field development around rapidly pitching airfoils[J].Journal of Fluids Engineering,1995,117(1):45-49.
[30]KATZ J,PLOTKIN A.Low-speed aerodynamics[M].New York:Cambridge University Press,2009:407-446.
[2]NOLL T,BROWN J,PEREZ-DAVIS M,et al.Investigation of the Helios prototype aircraft mishap report:Mishap Report Voume I[R].Washington,D.C.:NASA,2004.
[3]张健,张德虎.高空长航时太阳能无人机总体设计要点分析[J].航空学报,2016,37(S1):1-7.ZHANG J,ZHANG D H.Essentials of configuration design of HALE solar-powered UAVs[J].Acta Aeronautica et Astronautica Sinica,2016,37(S1):1-7(in Chinese).
[4]尹成越,高普云,郭健,等.“微风”(Zephyr7)无人机机翼力学性能分析[J].强度与环境,2012,39(3):19-25.YIN C Y,GAO P Y,GUO J,et al.Mechanical performance analysis on wing’s of Zephyr7UAV[J].Structure&Enviroment Engineering,2012,39(3):19-25(in Chinese).
[5]RAPINETT A.Zephyr:A high altitude long endurance unmanned air vehicle[D].Guildford:University of Surrey,2009:1-8.
[6]ALBERTSON J,TROUTT T,KEDZIE C.Unsteady aerodynamic forces at low airfoil pitching rates:AIAA-1988-2579[R].Reston,VA:AIAA,1988.
[7]HELIN H,WALKER J.Interrelated effects of pitch rate and pivot point on airfoil dynamic stall:AIAA-1985-0130[R].Reston,VA:AIAA,1985.
[8]WALKER J M,HELIN H E,STRICKLAND J H.An experimental investigation of an airfoil undergoing largeamplitude pitching motions[J].AIAA Journal,1985,23(8):1141-1142.
[9]SCHRECK S J,FALLER W E,ROBINSON M C.Unsteady separation processes and leading edge vortex precursors:Pitch rate and Reynolds number influences[J].Journal of Aircraft,2002,39(5):868-875.
[10]OI M V,ELDREDGE J D,WANG C.High-amplitude pitch of a flat plate:An abstraction of perching and flapping[J].International Journal of Micro Air Vehicles,2009,1(3):203-216.
[11]GOPALAKRISHNAN P,TAFTI D K.Effect of rotation kinematics and angle of attack on flapping flight[J].AIAA Journal,2009,47(11):2505-2519.
[12]LEKNYS R R,ARJOMANDI M,KELSO R M,et al.Dynamic-and post-stall characteristics of pitching airfoils at extreme conditions[J].Proceedings of the Institution of Mechanical Engineers,Part G:Journal of Aerospace Engineering,2018,232(6):1171-1185.
[13]高正红.绕振动机翼非定常气动力迟滞特性的模拟研究[J].应用数学和力学,1999,20(8):835-846.GAO Z H.Research on the hysteresis properties of unsteady aerodynamics about the oscillating wings[J].Applied Mathematics and Mechanics,1999,20(8):835-846(in Chinese).
[14]JUNG Y W,PARK S O.Vortex-shedding characteristics in the wake of an oscillating airfoil at low Reynolds number[J].Journal of Fluids and Structures,2005,20(3):451-464.
[15]YU Y,AMANDOLESE X,FAN C,et al.Experimental study and modelling of unsteady aerodynamic forces and moment on flat plate in high amplitude pitch ramp motion[J].Journal of Fluid Mechanics,2018,846:82-120.
[16]QIN S,KOOCHESFAHANI M,JABERI F.Large eddy simulations of unsteady flows over a stationary airfoil[J].Computers&Fluids,2018,161:155-170.
[17]YU H T,BERNAL L P.Effects of pivot location and reduced pitch rate on pitching rectangular flat plates[J].AIAA Journal,2017,55(3):702-718.
[18]EKATERINARIS J A,PLATZER M F.Computational prediction of airfoil dynamic stall[J].Progress in Aerospace Sciences,1998,33(11-12):759-846.
[19]张正秋,邹正平,刘火星,等.非失速二维振荡叶栅非定常流动数值模拟研究[J].空气动力学学报,2009,27(2):255-259.ZHANG Z Q,ZOU Z P,LIU H X,et al.A numericalstudy of unstalled two dimentional flow on an oscillating cascade[J].Acta Aerodynamica Sinica,2009,27(2):255-259(in Chinese).
[20]张正秋,邹正平,刘火星.振荡翼型非定常流动数值模拟研究[J].燃气涡轮试验与研究,2009,22(3):1-8.ZHANG Z Q,ZOU Z P,LIU H X.Numerical study oftwo dimensional flow on an oscillating airfoil[J].Gas Turbine Experiment and Research,2009,22(3):1-8(in Chinese).
[21]MENTER F R.Two-equation eddy-viscosity turbulence models for engineering applications[J].AIAA Journal,1994,32(8):1598-1605.
[22]VISBAL M R.Dynamic stall of a constant-rate pitching airfoil[J].Journal of Aircraft,1990,27(5):400-407.
[23]王科雷,祝小平,周洲,等.基于转捩模型的低雷诺数翼型优化设计研究[J].西北工业大学学报,2015,33(4):580-587.WANG K L,ZHU X P,ZHOU Z,et al.Studying optimization design of low Reynolds number airfoil using transition model[J].Journal of Northwestern Polytechnical University,2015,33(4):580-587(in Chinese).
[24]YANG Z,IGARASHI H,MARTIN M,et al.An experimental investigation on aerodynamic hysteresis of a lowReynolds number airfoil:AIAA-2008-0315[R].Reston,VA:AIAA,2008.
[25]PIZIALI R A.2-D and 3-D oscillating wing aerodynamics for a range of angles of attack including stall:NASA-TM-4632[R].Washington,D.C.:NASA,1994.
[26]MCALISTER K W,PUCCI S L,MCCROSKEY W J,et al.An experimental study of dynamic stall on advanced airfoil section.Volume 2:Pressure and force data:NASA-TM-84245-VOL-2[R].Washington,D.C.:NASA,1982.
[27]THEODORSEN T.General theory of aerodynamic instability and the mechanism of flutter:NACA-TR-496[R].Washington,D.C.:NASA,1949.
[28]叶正寅,张伟伟,史爱明.流固耦合力学基础及其应用[M].哈尔滨:哈尔滨工业大学出版社,2010:73-85.YE Z Y,ZHNAG W W,SHI A M.Fundamentals of fluid-solid coupling mechanics and its application[M].Harbin:Harbin Institute of Technology Press,2010:73-85(in Chinese).
[29]GENDRICH C P,KOOCHESFAHANI M M,VISBALM R.Effects of initial acceleration on the flow field development around rapidly pitching airfoils[J].Journal of Fluids Engineering,1995,117(1):45-49.
[30]KATZ J,PLOTKIN A.Low-speed aerodynamics[M].New York:Cambridge University Press,2009:407-446.