大迎角气动力数值模拟及建模研究
|
摘要
大迎角飞行与机动是现代战斗机的重要特征之一,能够准确地模拟大迎角非定常流场结构及预测相应的大迎角非定常气动力特性,对现代战斗机及其控制系统的设计至关重要。本文采用数值计算方法,通过求解三维N-S方程,分别对绕机翼、机翼-机身-鸭翼组合体大迎角流场结构及气动力特性进行数值模拟与分析,得到了良好的数值模拟结果。同时,为了满足飞行器大迎角机动飞行动力学特性研究的需要,本文在对大迎角气动力进行数值模拟的基础上,开展了相应的大迎角动态气动力特性的建模研究。
主要完成了以下几方面的工作:
1 采用数值计算方法,对亚音速三角翼静态纵向及带有小侧滑和横侧小扰动情况下的流场及相应的气动特性进行了计算,利用数值计算所得到的大迎角流动流场数据,根据实验研究结果及流场拓朴理论,建立了用于大迎角旋涡流场结构特性分析的方法。给出了三角翼大迎角情况下相应的气动力、力矩系数,以及机翼前缘分离涡轴线位置和旋涡破裂位置随迎角的变化规律,并对带有小侧滑和横侧小扰动情况下对横侧力矩的影响进行了计算与分析。计算结果表明与实验结果符合较好。
2 采用数值计算方法,对三角翼进行大迎角俯仰机动过程中的动态流场结构进行了计算,分析了俯仰角速度对流场结构和气动力系数的影响。在此基础上,对三角翼在上仰过程中受到横侧小扰动情况下的流场结构和气动力特性进行了计算研究。给出了三角翼纵向动态情况下的气动力系数变化,特别是大迎角横侧力矩系数的变化特征,并对受到横侧小扰动后,可能引发的横侧运动不稳定现象进行了分析。结果表明,机翼的上仰运动延迟了机翼上翼面旋涡的破裂,同时,随着机翼俯仰角速度的提高,机翼抵抗旋涡非对称破裂的能力明显增强,从而使得机翼在运动过程中,抵抗非操纵横侧偏离的能力明显提高。
3 采用数值计算方法,对绕机翼-机身-鸭翼组合体亚音速静态大迎角流场及气动力特性进行了计算。通过计算分析说明,在一定迎角下,前机身涡、边条
Current and future fighter airplanes are designed to transiently fly at very high angles of attack and require highly maneuverability. So it is very important to simulate the corresponding flowfield structure and predict the aerodynamics of aircrafts accurately in the designation of modern fighter aircrafts and their control systems. In this paper, three-dimensional Navier-Strokes numerical simulations were carried out to predict the characteristics of the vortex-dominated flowfield over delta wings and a wing-body-canard. Besides, according to state-space model that was proposed by Goman, some research work is developed to simulate the unsteady aerodynamics at high angles of attack. And the corresponding data from Navier-Strokes numerical simulations is used for the identification of the unsteady aerodynamic description. The main work developed in this paper is as follows:1. Numerical investigation of the structure of the vortical flowfield over delta wings at high angles of attack in longitudinal and with small sideslip angle is presented here. The methods that analyze the flowfield structure qualitatively and quantitatively are given by using flowfield data from the computational results. In the region before the vortex breakdown, the vortex axes are approximated as being straight line. As the angle of attack increases, the vortex axes are closer to the root chord, and far away from the wing surface. Along the vortex axes, as the adverse pressure gradients occur, the axial velocity decreases, the vortex becomes unstable, and it is possible to breakdown. The occurrence of the breakdown results in the instability of lateral motion for a delta wing, and the lateral moment diverges after a small disturbance occurs.2. Numerical investigation of the structure of the vortical flowfield over a delta wing undergoing maneuverable motions is presented. Three cases are considered to investigate the frequency effect on the flowfield structure and aerodynamic loads for
the delta wing. The lateral moments are more evident as the frequency decreases at high angles of attack. Pitching motion with high frequency delays the vortex breakdown obviously. Besides, the influences of a transient lateral disturbance on the lateral aerodynamics are researched in the paper. For lower frequency case, the lateral moment diverges even if the disturbance occurs at an angle of attack at which the vortex do not breakdown over the wing. As the frequency increases, the lateral moment has no evident change after the transient lateral disturbance occurs, and the lateral-directional stability is more pronounced.3. The static flowfield over a wing-body-canard is calculated and the vortex flow over the fore-body, strake, canard and wings is analyzed. The influence of the vortex flows on each other is also discussed.4. The dynamic flowfield over the wing-body-canard is calculated and the influence of the reduced frequency on the flowfield and the aerodynamics is analyzed.5. According to the aerodynamic characteristics of aircrafts, the state-space model of unsteady aerodynamics at high angles of attack is established. And the unknown parameters in the aerodynamic model are identified by system identification method. The maximum likelihood method is used as identification principle, and the identified arithmetic is Newton-Raphson method. The results show that the model can describe the unsteady aerodynamics at high angles of attack very well.6. The research about the aerodynamic model establishment is one of the basic research for flight dynamics, the designation of modern fighter aircrafts and their control systems. In this paper, the aerodynamic model method integrates with the numerical simulation to avoid great quantity computations of unsteady aerodynamics. The integration of these two methods is a rather effective, economical and practical method.
主要完成了以下几方面的工作:
1 采用数值计算方法,对亚音速三角翼静态纵向及带有小侧滑和横侧小扰动情况下的流场及相应的气动特性进行了计算,利用数值计算所得到的大迎角流动流场数据,根据实验研究结果及流场拓朴理论,建立了用于大迎角旋涡流场结构特性分析的方法。给出了三角翼大迎角情况下相应的气动力、力矩系数,以及机翼前缘分离涡轴线位置和旋涡破裂位置随迎角的变化规律,并对带有小侧滑和横侧小扰动情况下对横侧力矩的影响进行了计算与分析。计算结果表明与实验结果符合较好。
2 采用数值计算方法,对三角翼进行大迎角俯仰机动过程中的动态流场结构进行了计算,分析了俯仰角速度对流场结构和气动力系数的影响。在此基础上,对三角翼在上仰过程中受到横侧小扰动情况下的流场结构和气动力特性进行了计算研究。给出了三角翼纵向动态情况下的气动力系数变化,特别是大迎角横侧力矩系数的变化特征,并对受到横侧小扰动后,可能引发的横侧运动不稳定现象进行了分析。结果表明,机翼的上仰运动延迟了机翼上翼面旋涡的破裂,同时,随着机翼俯仰角速度的提高,机翼抵抗旋涡非对称破裂的能力明显增强,从而使得机翼在运动过程中,抵抗非操纵横侧偏离的能力明显提高。
3 采用数值计算方法,对绕机翼-机身-鸭翼组合体亚音速静态大迎角流场及气动力特性进行了计算。通过计算分析说明,在一定迎角下,前机身涡、边条
Current and future fighter airplanes are designed to transiently fly at very high angles of attack and require highly maneuverability. So it is very important to simulate the corresponding flowfield structure and predict the aerodynamics of aircrafts accurately in the designation of modern fighter aircrafts and their control systems. In this paper, three-dimensional Navier-Strokes numerical simulations were carried out to predict the characteristics of the vortex-dominated flowfield over delta wings and a wing-body-canard. Besides, according to state-space model that was proposed by Goman, some research work is developed to simulate the unsteady aerodynamics at high angles of attack. And the corresponding data from Navier-Strokes numerical simulations is used for the identification of the unsteady aerodynamic description. The main work developed in this paper is as follows:1. Numerical investigation of the structure of the vortical flowfield over delta wings at high angles of attack in longitudinal and with small sideslip angle is presented here. The methods that analyze the flowfield structure qualitatively and quantitatively are given by using flowfield data from the computational results. In the region before the vortex breakdown, the vortex axes are approximated as being straight line. As the angle of attack increases, the vortex axes are closer to the root chord, and far away from the wing surface. Along the vortex axes, as the adverse pressure gradients occur, the axial velocity decreases, the vortex becomes unstable, and it is possible to breakdown. The occurrence of the breakdown results in the instability of lateral motion for a delta wing, and the lateral moment diverges after a small disturbance occurs.2. Numerical investigation of the structure of the vortical flowfield over a delta wing undergoing maneuverable motions is presented. Three cases are considered to investigate the frequency effect on the flowfield structure and aerodynamic loads for
the delta wing. The lateral moments are more evident as the frequency decreases at high angles of attack. Pitching motion with high frequency delays the vortex breakdown obviously. Besides, the influences of a transient lateral disturbance on the lateral aerodynamics are researched in the paper. For lower frequency case, the lateral moment diverges even if the disturbance occurs at an angle of attack at which the vortex do not breakdown over the wing. As the frequency increases, the lateral moment has no evident change after the transient lateral disturbance occurs, and the lateral-directional stability is more pronounced.3. The static flowfield over a wing-body-canard is calculated and the vortex flow over the fore-body, strake, canard and wings is analyzed. The influence of the vortex flows on each other is also discussed.4. The dynamic flowfield over the wing-body-canard is calculated and the influence of the reduced frequency on the flowfield and the aerodynamics is analyzed.5. According to the aerodynamic characteristics of aircrafts, the state-space model of unsteady aerodynamics at high angles of attack is established. And the unknown parameters in the aerodynamic model are identified by system identification method. The maximum likelihood method is used as identification principle, and the identified arithmetic is Newton-Raphson method. The results show that the model can describe the unsteady aerodynamics at high angles of attack very well.6. The research about the aerodynamic model establishment is one of the basic research for flight dynamics, the designation of modern fighter aircrafts and their control systems. In this paper, the aerodynamic model method integrates with the numerical simulation to avoid great quantity computations of unsteady aerodynamics. The integration of these two methods is a rather effective, economical and practical method.
引文
[1] 杨小平.飞机超大迎角非线性气动力建模和辨识.西北工业大学博士学位论文.1998年
[2] 朱自强,陈炳永,李津.现代飞机设计中的空气动力学.北京航空航天大学出版社.1995年.P6.
[3] 刘谋佶,吕志咏,丘成昊,等.边条翼与旋涡分离流[M].北京:北京航空学院出版社,1988.p51.
[4] Canter D., "X-31 Post-Stall Envelope Expansion and Tactical Utility Testing", 4th NASA High Alpha Conference. July, 1994.
[5] Skow, A. M., "An Analysis of the Su-27 Flight Demonstration at the 1989 Paris Air Show," AAE Paper 901001 Apr. 1990.
[6] W.B. Herbst. Future Fighter Technologies. J. Aircraft. Vol. 17, No. 8, August, 1980
[7] Gallaway, C. R. and Osborn, R. F. , "Aerodynamics Prospective of Supermaneuverability," AIAA Paper 85-4068. Oct. 1985.
[8] 高正红,焦天峰.飞行器快速俯仰产生大迎角非定常气动力数学模型研究.西北工业大学学报.Vol.19 No.4 p506-510 2001.
[9] E.J. Jumper, S.J. Shreck, R.L. Dimmick. Lift-Curve Characteristics for an Airfoil Pitching at Constant Rate. AIAA-86-0117
[10] M. R. Soltani, M. B. Bragg, and J. M. Brandon, "Measurements on an Oscillating 70-Deg Delta Wing in Subsonic Flow," J. Aircraft Vol. 27, No. 3, March 1990
[11] Thompson, S. A., Batill, S. M. and Nelson, R. C., "Separated Flowfield on a Slender Wing Undergoing Transient Pitching Motions", Journal of Aircraft, Vol. 28, Aug. 1991, pp. 489-495
[12] Huyer, S. A., Robinson, M. C. and Luttges, M. W., "Unsteady Aerodynamic Loading Produced by a Sinusoidally Oscillating Delta Wing," Journal of Aircraft, Vol. 29, No. 3, May-June 1992
[13] W. H. Stahl, M. Mahmood and A. Asghar, "Experimental Investigations of the Vortex Flow on Delta Wings at High Incidence", AIAA JOURNAL Vol. 30, No. 4, April 1992
[14] G. Guglieri and F. B. Guagliotti, "Experimental Investigation of Vortex Dynamics on Delta Wings", AIAA-92-2731-CP
[15] Soltani, M. R. and Bragg, M. B., "Early Vortex Burst on a Delta Wing in Pitch", AIAA Journal Vol. 31, No. 12, December 1993
[16] Traub, L. W., Rediniotis, O. K., Klute, S. M., Moore, C. T. and Telionis, D. P., "Instabilities of Vortex Breakdown: Their Structure and Growth," AIAA Paper 95-2308, 1995
[17] Addington, G. A., Hanff, E. S. and Nelson, R. C., "Leading-Edge Vortex Behavior in the Vicinity of a Delta Wing Apex," AIAA-96-3388-CP
[18] Gregory A. Addington and Robert C. Nelson, "The Correspondence between Flow-Field Structure and Critical States on a 65-Degree Delta Wing", AIAA-98-4520
[19] A. Mitchell, P. Molton, D. barberis and J. Délery. "Characterization of Vortex Breakdown by Flow Field and Surface Measurements", AIAA-2000-O788
[20] N. G. Verhaagen and C. E. Jobe. "Study on a 65-deg Delta Wing at Sideslip", AIAA-2001-0691
[21] Lars E. Ericsson. Nonlinear Unsteady Aerodynamics of Pitching Delta Wings. AIAA-98-2518
[22] Ericsson, L. E., "Effect of Pitch Rate on Delta Wing Vortex Characteristics," AIAA Paper 96-3405, Aug. 1995
[23] Huang, X.Z., Sun, Y.Z. and Hanff, E.S., "Further Investigations of Leading-Edge Vortex Breakdown Over Delta Wings," AIAA Paper-97-2263, 1997
[24] 杨晓锋,赵小虎,等.细长三角翼的摇滚特性.空气动力学报.Vol.18,No.1,Mar.,2000
[25] 黄达,李志强,史志伟,吴根兴.飞机大振幅非定常滚转运动的非线性稳定性分析.空气动力学报.Vol.18,No.4,Dec.,2000
[26] 张祖庚.三角翼大迎角俯仰振动实验研究.航空部第626研究所.1994.
[27] 杨希明.大迎角80°前缘后掠平板三角翼摇滚现象实验研究.航空部第626研究所.1991.
[28] 邓学荧.前体非对称涡流动及其扰动主动控制.空气动力学前沿研究论文集.2003.
[29] 姜裕标,黄勇,孙海生,等.非定常气动力及控制技术风洞试验研究.空气动力学前沿研究论文集.2003.
[30] Klein V., Batterson J. 6., Murphy P.C.. Determination of Model Structure and Parameters of an Airplane from Pre-and Post-Stall Flight. Data. AIAA 81-1866, 1981
[31] EugeneA. Morelli and Vladislav Klein, "Determination the Accuracy of Aerodynamic Model Parameters Estimated From Flight Test Data," AIAA Paper-95-3499-CP
[32] Patrick C. Murphy and Vladislav Klein, "Estimation of Aircraft Unsteady Aerodynamic Parameters from Dynamic Wind Tunnel Testing", AIAA-2001-4016
[33] Murray Tobak, Lewis B. Schiff. On the Formulation of the Aerodynamic Characteristics in Aircraft Dynamics. NASA TR R-456
[34] M. Goman, A. Khrabrov. State-Space Representation of Aerodynamic Characteristics of an Aircraft at High Angles of Attack. Journal of Aircraft. Vol. 31, No. 5, Sept.-oct., 1994
[35] M. G. Goman, A.V. Khramtsovsky. Global stability analysis of nonlinear aircraft dynamics. AIAA 97-3721. AIAA Atmospheric Fight Mechanics Conference, New Orleans, LA, Aug. 11-13, 1997
[36]M. G. Goman, E. N. Kolesnikov. Robust nonlinear dynamic inversion method for an aircraft motion control. AIAA 98-4208. AIAA Guidance, Navigation, and Control Conference and Exhibit. Boston, MA. Aug. 10-12, 1998
[37]N. B. Abramov, M. G. Goman, A. N. Khrabrov, K. A. Kolinko. Simple Wings Unsteady Aerodynamics at High Angles of Attack: Experimental and Modeling Results. AIAA 99-4013. AIAA Atmospheric Flight Mechanics Conference and Exhibit, Portland OR. Aug. 9-11, 1999
[38]GomanM. G., Greenwell D. I. and Khrabrov A. N., "The Characteristic Time Constant Approach for Mathematical Modeling of High Angle of Attack Aerodynamics" , ICAS Paper, 22nd Congress of the Aeronautical Sciences. Sept. 2000, Harrogate, UK, pp. 223. 1-223.14.
[39]Abramov N. B., Goman M. G., Greenwell D. I. And Khrabrov A. N., "Two-Step Linear Regression Method for Identication of High Incidence Unsteady Aerodynamic Model" , AIAA-2001-4080
[40]Zhongjun Wang, C.Edward Lan, Jay M. Brandon. Fuzzy Logic Modeling of Nonlinear Unsteady Aerodynamics. AIAA-98-4351
[41]Jian Tan, Hong Xie, and Yung-Cheng Lee. Efficient Establishment of a Fuzzy Logic Model for Process Modeling and Control. IEEE Transactions on Semiconductor Manufacturing. Vol.8, No.1, Feb, 1995
[42]Tomohiro Takagi and Michio Sugeno. Fuzzy Identification of Systems and Its Applications to Modeling and Control. IEEE Transactions on Systems , Man and Cybernetics, VOL.SME-15, No.1, January/February 1985
[43]Lawrence W.Taylor, Jr., Kenneth W. IIiff, and Bruce G. Powers. A Comparison of Newton-Raphson and Other Methods for Determining Stability Derivatives From Flight Data. AIAA 69-315
[14] Chien-Chung Hu, C. Edward Lan, Jay Brandon. Unsteady Aerodynamic Models For Maneuvering Aircraft. AIAA-93-3626-CP
[45] Grismer, D. S. and Jenkins, J. E., "Critical-State Transients for a Rolling 65° Delta Wing," AIAA Paper 96-2432, June 1996
[46] D. Fischenberg. Identification of an Unsteady Aerodynamic Stall Model from Flight Test Data. AIAA-95-3438-CP
[47] Jay M. Brandon and John V. Foster, "Recent Dynamic Measurements and Considerations for Aerodynamic Modeling of Fighter Airplane Configurations", AIAA-98-4447
[48] X. Z. Huang, H. Y. Lou and E. S. Hanff. "Non-Linear Indicial Response Response and Internal State-Space Representation for Free-to-Roll Trajectory Prediction of a 65° Delta wing at High Incidence" ,AIAA-2002-4713
[49] X. Z. Huang and E. S. Hanff. "Hysteresis and Bifurcation Analysis of a Fighter and a Delta wing at High Incidence" ,AIAA-2002-4714
[50] 史志伟,吴根兴.飞机大迎角滚转运动频率域建模与稳定性分析.空气动力学报.Vol.18,No.3,Sept.,2000.
[51] 汪清.飞机大攻角非定常气动力建模及其应用研究.西北工业大学博士学位论文.1994年12月.
[52] 高正红.绕振动机翼非定常气动力迟滞特性的模拟研究.应用数学和力学.Vol.20 No.8 p835-846 1999.
[53] 李树有,王启,张培田.飞机失速/尾旋特性的预测和试验研究.飞行力学Vol.18 No.3 2000.
[54] 蔡金狮,等.飞行器系统辨识.宇航出版社,1995.
[55] 吴江航,韩庆书.计算流体力学的理论、方法及应用.科学出版社.1988年.p2.
[56] 傅德薰,汪翼云,马延文,等.计算空气动力学.宇航出版社.1987年.p4.
[57] Jameson, A., "Successes and Challenges in Computational Aerodynamics", AIAA Paper 87-1184, 1987.
[58] Kozo Fujii and Lewis B. Schiff, "Numerical Simulation of Vortical Flows Over a Strake-Delta Wing", AIAA JOURNAL 1989. Vol. 27, No. 9, pp 1153-1162.
[59] Shreekant Agrawal, Raymond Matt Barnett, and Brian Anthony Robinson, "Numerical Investigation of Vortex Breakdown on a Delta Wing", AIAA JOURNAL Vol. 30, No. 3, March 1992
[60] Papadakis, M., Phillis, D. And Liu, X., "Experimental and Numerical Delta Wing Study at High Angles of Attack and Sideslip", AIAA-92-2713
[61] Ekaterinaris. J. A. and Schiff. L. B., "Numerical Simulation of the Effects of Variation of Angles of Attack and Sweep Angle on Vortex Breakdown over Delta Wings", AIAA-90-3000-CP
[62] Joseph Vadyak and David M. Schuster, "Navier-Stokes Simulation of Burst Vortex Flowfields for Fighter Aircraft at High Incidence", Journal of Aircraft, Vol. 28, No. 10, 1991, pp. 638-645
[63] Gordnier, R. E., "Computational Study of a Turbulent Delta-Wing Flowfield Using Two-Equation Turbulence Models," AIAA Paper-96-2076
[64] Z. Rusak and D. Lamb. "Prediction of Vortex Breakdown in Leading Edge Vortices above Slender Delta Wings", AIAA-1998-2860
[65] J. Muller and D. Hummel. "Time-Accurate CFD Analysis of the Unsteady Flow on a Fixed Delta Wing", AIAA-2000-0138
[66] Scott A. Morton and James R. Forsythe, "Analysis of Delta Wing Vortical Substructures Using Detached-Eddy Simulation", AIAA-2002-2968
[67] 张涵信.亚、声速旋涡流动特征的定性分析研究.空气动力学学报.Vol.13,No.3,1995
[68] 张涵信,邓小刚.三维定常分离流和涡运动的定性分析研究.空气动力学学报.Vol.10,No.1,1992
[69] 林炳秋.细长三角翼前缘分离涡破裂特性计算方法.空气动力学学报.1985年第3期.
[70] 是勋刚.旋涡破裂的数值模拟.空气动力学学报.1985年第1期.
[71] 高正红.关于绕任意机翼非定常流动的一种无条件稳定的欧拉方程解[J].应用数学和力学.1995,16(12):1123-1134.
[72] 郭广利.跨音速定常与非定常粘性绕流的数值模拟.西北工业大学博士学位论文.1996年11月.
[73] Yahia A. Abdelhamid and Osama A. Kandil, "Effect of Reduced Frequency on Super Maneuver Delta Wing", AIAA 98-0415
[74] Y. Le Moigne, A. Rizzi, and P. Johansson. "CFD Simulations of a Delta Wing in High Alpha Pitch Oscillations", AIAA-2001-0862
[75] Gao Zhenghong. "Research on the Hysteresis Properties of Unsteady Aerodynamics about the Oscillating Wings", Applied Mathematics and Mechanics. Vol. 20, No. 8, Aug. 1999.
[76] I. Gursul. "A Proposed Mechanism for the Time Lag of Vortex Breakdown Location in Unsteady Flows", AIAA-2000-0787
[77] 张廷芳.计算流体力学.大连理工大学出版社.1992.
[78] Jameson, A., Schmidt, W. and Turkel, E., "Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time Stepping Scheme," AIAA Paper 81-1259, 1981.
[79] 何雄.跨音速机翼静气动弹性研究.西北工业大学博士学位论文.1991年4月.
[80] 万敏.大迎角定常/非定常气动力数值模拟.西北工业大学硕士学位论文.1999年3月.
[81] 肖志祥,李凤蔚,鄂秦.湍流模型在翼身组合体流场数值模拟中的应用研究.西北工业大学学报.Vol.21 No.1 2003.
[82] 李凤蔚,肖志祥.三种湍流模型模拟能力的对比.西北工业大学学报.Vol.20 No.3 2002
[83] Yang X. D., Ma H. Y. and Huang Y. N., "Prediction of Homogeneous Shear Flow and a Backward-Facing Step Flow with Some Linear and Non-linear K-ε Turbulence Models", Communication in Nonlinear Sciences and Numerical Simulation. November 2003
[84] David Degani, Lewis B. Schiff, "Computation of Turbulent Supersonic Flows around Pointed Bodies Having Crossflow Separation", Journal of Computational Physics 66, 173-196(1986)
[85] 杨云军,崔尔杰,周伟江.细长体大迎角非对称涡流数值模拟及形成机理的探讨.空气动力学会议论文集.中国宇航出版社.2003年10月
[86] 许洲.第四代战斗机空战仿真系统研究.西北工业大学博士学位论文.2001年.
[87] 蔡金狮.动力学系统辨识与建模.国防工业出版社,1991
[88] Yigang Fan and Frederick H. Lutze. Identification of an Unsteady Aerodynamic Model at High Angles of Attack. AIAA-96-3407-CP
[89] 焦天峰.大迎角非定常气动力数学模型研究.西北工业大学硕士学位论文.2000年3月.
[90] 陆璇.数理统计基础.清华大学出版社,1998.
[91] 张成乾,张国强.系统辨识与参数估计.机械工业出版社,1986
[2] 朱自强,陈炳永,李津.现代飞机设计中的空气动力学.北京航空航天大学出版社.1995年.P6.
[3] 刘谋佶,吕志咏,丘成昊,等.边条翼与旋涡分离流[M].北京:北京航空学院出版社,1988.p51.
[4] Canter D., "X-31 Post-Stall Envelope Expansion and Tactical Utility Testing", 4th NASA High Alpha Conference. July, 1994.
[5] Skow, A. M., "An Analysis of the Su-27 Flight Demonstration at the 1989 Paris Air Show," AAE Paper 901001 Apr. 1990.
[6] W.B. Herbst. Future Fighter Technologies. J. Aircraft. Vol. 17, No. 8, August, 1980
[7] Gallaway, C. R. and Osborn, R. F. , "Aerodynamics Prospective of Supermaneuverability," AIAA Paper 85-4068. Oct. 1985.
[8] 高正红,焦天峰.飞行器快速俯仰产生大迎角非定常气动力数学模型研究.西北工业大学学报.Vol.19 No.4 p506-510 2001.
[9] E.J. Jumper, S.J. Shreck, R.L. Dimmick. Lift-Curve Characteristics for an Airfoil Pitching at Constant Rate. AIAA-86-0117
[10] M. R. Soltani, M. B. Bragg, and J. M. Brandon, "Measurements on an Oscillating 70-Deg Delta Wing in Subsonic Flow," J. Aircraft Vol. 27, No. 3, March 1990
[11] Thompson, S. A., Batill, S. M. and Nelson, R. C., "Separated Flowfield on a Slender Wing Undergoing Transient Pitching Motions", Journal of Aircraft, Vol. 28, Aug. 1991, pp. 489-495
[12] Huyer, S. A., Robinson, M. C. and Luttges, M. W., "Unsteady Aerodynamic Loading Produced by a Sinusoidally Oscillating Delta Wing," Journal of Aircraft, Vol. 29, No. 3, May-June 1992
[13] W. H. Stahl, M. Mahmood and A. Asghar, "Experimental Investigations of the Vortex Flow on Delta Wings at High Incidence", AIAA JOURNAL Vol. 30, No. 4, April 1992
[14] G. Guglieri and F. B. Guagliotti, "Experimental Investigation of Vortex Dynamics on Delta Wings", AIAA-92-2731-CP
[15] Soltani, M. R. and Bragg, M. B., "Early Vortex Burst on a Delta Wing in Pitch", AIAA Journal Vol. 31, No. 12, December 1993
[16] Traub, L. W., Rediniotis, O. K., Klute, S. M., Moore, C. T. and Telionis, D. P., "Instabilities of Vortex Breakdown: Their Structure and Growth," AIAA Paper 95-2308, 1995
[17] Addington, G. A., Hanff, E. S. and Nelson, R. C., "Leading-Edge Vortex Behavior in the Vicinity of a Delta Wing Apex," AIAA-96-3388-CP
[18] Gregory A. Addington and Robert C. Nelson, "The Correspondence between Flow-Field Structure and Critical States on a 65-Degree Delta Wing", AIAA-98-4520
[19] A. Mitchell, P. Molton, D. barberis and J. Délery. "Characterization of Vortex Breakdown by Flow Field and Surface Measurements", AIAA-2000-O788
[20] N. G. Verhaagen and C. E. Jobe. "Study on a 65-deg Delta Wing at Sideslip", AIAA-2001-0691
[21] Lars E. Ericsson. Nonlinear Unsteady Aerodynamics of Pitching Delta Wings. AIAA-98-2518
[22] Ericsson, L. E., "Effect of Pitch Rate on Delta Wing Vortex Characteristics," AIAA Paper 96-3405, Aug. 1995
[23] Huang, X.Z., Sun, Y.Z. and Hanff, E.S., "Further Investigations of Leading-Edge Vortex Breakdown Over Delta Wings," AIAA Paper-97-2263, 1997
[24] 杨晓锋,赵小虎,等.细长三角翼的摇滚特性.空气动力学报.Vol.18,No.1,Mar.,2000
[25] 黄达,李志强,史志伟,吴根兴.飞机大振幅非定常滚转运动的非线性稳定性分析.空气动力学报.Vol.18,No.4,Dec.,2000
[26] 张祖庚.三角翼大迎角俯仰振动实验研究.航空部第626研究所.1994.
[27] 杨希明.大迎角80°前缘后掠平板三角翼摇滚现象实验研究.航空部第626研究所.1991.
[28] 邓学荧.前体非对称涡流动及其扰动主动控制.空气动力学前沿研究论文集.2003.
[29] 姜裕标,黄勇,孙海生,等.非定常气动力及控制技术风洞试验研究.空气动力学前沿研究论文集.2003.
[30] Klein V., Batterson J. 6., Murphy P.C.. Determination of Model Structure and Parameters of an Airplane from Pre-and Post-Stall Flight. Data. AIAA 81-1866, 1981
[31] EugeneA. Morelli and Vladislav Klein, "Determination the Accuracy of Aerodynamic Model Parameters Estimated From Flight Test Data," AIAA Paper-95-3499-CP
[32] Patrick C. Murphy and Vladislav Klein, "Estimation of Aircraft Unsteady Aerodynamic Parameters from Dynamic Wind Tunnel Testing", AIAA-2001-4016
[33] Murray Tobak, Lewis B. Schiff. On the Formulation of the Aerodynamic Characteristics in Aircraft Dynamics. NASA TR R-456
[34] M. Goman, A. Khrabrov. State-Space Representation of Aerodynamic Characteristics of an Aircraft at High Angles of Attack. Journal of Aircraft. Vol. 31, No. 5, Sept.-oct., 1994
[35] M. G. Goman, A.V. Khramtsovsky. Global stability analysis of nonlinear aircraft dynamics. AIAA 97-3721. AIAA Atmospheric Fight Mechanics Conference, New Orleans, LA, Aug. 11-13, 1997
[36]M. G. Goman, E. N. Kolesnikov. Robust nonlinear dynamic inversion method for an aircraft motion control. AIAA 98-4208. AIAA Guidance, Navigation, and Control Conference and Exhibit. Boston, MA. Aug. 10-12, 1998
[37]N. B. Abramov, M. G. Goman, A. N. Khrabrov, K. A. Kolinko. Simple Wings Unsteady Aerodynamics at High Angles of Attack: Experimental and Modeling Results. AIAA 99-4013. AIAA Atmospheric Flight Mechanics Conference and Exhibit, Portland OR. Aug. 9-11, 1999
[38]GomanM. G., Greenwell D. I. and Khrabrov A. N., "The Characteristic Time Constant Approach for Mathematical Modeling of High Angle of Attack Aerodynamics" , ICAS Paper, 22nd Congress of the Aeronautical Sciences. Sept. 2000, Harrogate, UK, pp. 223. 1-223.14.
[39]Abramov N. B., Goman M. G., Greenwell D. I. And Khrabrov A. N., "Two-Step Linear Regression Method for Identication of High Incidence Unsteady Aerodynamic Model" , AIAA-2001-4080
[40]Zhongjun Wang, C.Edward Lan, Jay M. Brandon. Fuzzy Logic Modeling of Nonlinear Unsteady Aerodynamics. AIAA-98-4351
[41]Jian Tan, Hong Xie, and Yung-Cheng Lee. Efficient Establishment of a Fuzzy Logic Model for Process Modeling and Control. IEEE Transactions on Semiconductor Manufacturing. Vol.8, No.1, Feb, 1995
[42]Tomohiro Takagi and Michio Sugeno. Fuzzy Identification of Systems and Its Applications to Modeling and Control. IEEE Transactions on Systems , Man and Cybernetics, VOL.SME-15, No.1, January/February 1985
[43]Lawrence W.Taylor, Jr., Kenneth W. IIiff, and Bruce G. Powers. A Comparison of Newton-Raphson and Other Methods for Determining Stability Derivatives From Flight Data. AIAA 69-315
[14] Chien-Chung Hu, C. Edward Lan, Jay Brandon. Unsteady Aerodynamic Models For Maneuvering Aircraft. AIAA-93-3626-CP
[45] Grismer, D. S. and Jenkins, J. E., "Critical-State Transients for a Rolling 65° Delta Wing," AIAA Paper 96-2432, June 1996
[46] D. Fischenberg. Identification of an Unsteady Aerodynamic Stall Model from Flight Test Data. AIAA-95-3438-CP
[47] Jay M. Brandon and John V. Foster, "Recent Dynamic Measurements and Considerations for Aerodynamic Modeling of Fighter Airplane Configurations", AIAA-98-4447
[48] X. Z. Huang, H. Y. Lou and E. S. Hanff. "Non-Linear Indicial Response Response and Internal State-Space Representation for Free-to-Roll Trajectory Prediction of a 65° Delta wing at High Incidence" ,AIAA-2002-4713
[49] X. Z. Huang and E. S. Hanff. "Hysteresis and Bifurcation Analysis of a Fighter and a Delta wing at High Incidence" ,AIAA-2002-4714
[50] 史志伟,吴根兴.飞机大迎角滚转运动频率域建模与稳定性分析.空气动力学报.Vol.18,No.3,Sept.,2000.
[51] 汪清.飞机大攻角非定常气动力建模及其应用研究.西北工业大学博士学位论文.1994年12月.
[52] 高正红.绕振动机翼非定常气动力迟滞特性的模拟研究.应用数学和力学.Vol.20 No.8 p835-846 1999.
[53] 李树有,王启,张培田.飞机失速/尾旋特性的预测和试验研究.飞行力学Vol.18 No.3 2000.
[54] 蔡金狮,等.飞行器系统辨识.宇航出版社,1995.
[55] 吴江航,韩庆书.计算流体力学的理论、方法及应用.科学出版社.1988年.p2.
[56] 傅德薰,汪翼云,马延文,等.计算空气动力学.宇航出版社.1987年.p4.
[57] Jameson, A., "Successes and Challenges in Computational Aerodynamics", AIAA Paper 87-1184, 1987.
[58] Kozo Fujii and Lewis B. Schiff, "Numerical Simulation of Vortical Flows Over a Strake-Delta Wing", AIAA JOURNAL 1989. Vol. 27, No. 9, pp 1153-1162.
[59] Shreekant Agrawal, Raymond Matt Barnett, and Brian Anthony Robinson, "Numerical Investigation of Vortex Breakdown on a Delta Wing", AIAA JOURNAL Vol. 30, No. 3, March 1992
[60] Papadakis, M., Phillis, D. And Liu, X., "Experimental and Numerical Delta Wing Study at High Angles of Attack and Sideslip", AIAA-92-2713
[61] Ekaterinaris. J. A. and Schiff. L. B., "Numerical Simulation of the Effects of Variation of Angles of Attack and Sweep Angle on Vortex Breakdown over Delta Wings", AIAA-90-3000-CP
[62] Joseph Vadyak and David M. Schuster, "Navier-Stokes Simulation of Burst Vortex Flowfields for Fighter Aircraft at High Incidence", Journal of Aircraft, Vol. 28, No. 10, 1991, pp. 638-645
[63] Gordnier, R. E., "Computational Study of a Turbulent Delta-Wing Flowfield Using Two-Equation Turbulence Models," AIAA Paper-96-2076
[64] Z. Rusak and D. Lamb. "Prediction of Vortex Breakdown in Leading Edge Vortices above Slender Delta Wings", AIAA-1998-2860
[65] J. Muller and D. Hummel. "Time-Accurate CFD Analysis of the Unsteady Flow on a Fixed Delta Wing", AIAA-2000-0138
[66] Scott A. Morton and James R. Forsythe, "Analysis of Delta Wing Vortical Substructures Using Detached-Eddy Simulation", AIAA-2002-2968
[67] 张涵信.亚、声速旋涡流动特征的定性分析研究.空气动力学学报.Vol.13,No.3,1995
[68] 张涵信,邓小刚.三维定常分离流和涡运动的定性分析研究.空气动力学学报.Vol.10,No.1,1992
[69] 林炳秋.细长三角翼前缘分离涡破裂特性计算方法.空气动力学学报.1985年第3期.
[70] 是勋刚.旋涡破裂的数值模拟.空气动力学学报.1985年第1期.
[71] 高正红.关于绕任意机翼非定常流动的一种无条件稳定的欧拉方程解[J].应用数学和力学.1995,16(12):1123-1134.
[72] 郭广利.跨音速定常与非定常粘性绕流的数值模拟.西北工业大学博士学位论文.1996年11月.
[73] Yahia A. Abdelhamid and Osama A. Kandil, "Effect of Reduced Frequency on Super Maneuver Delta Wing", AIAA 98-0415
[74] Y. Le Moigne, A. Rizzi, and P. Johansson. "CFD Simulations of a Delta Wing in High Alpha Pitch Oscillations", AIAA-2001-0862
[75] Gao Zhenghong. "Research on the Hysteresis Properties of Unsteady Aerodynamics about the Oscillating Wings", Applied Mathematics and Mechanics. Vol. 20, No. 8, Aug. 1999.
[76] I. Gursul. "A Proposed Mechanism for the Time Lag of Vortex Breakdown Location in Unsteady Flows", AIAA-2000-0787
[77] 张廷芳.计算流体力学.大连理工大学出版社.1992.
[78] Jameson, A., Schmidt, W. and Turkel, E., "Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time Stepping Scheme," AIAA Paper 81-1259, 1981.
[79] 何雄.跨音速机翼静气动弹性研究.西北工业大学博士学位论文.1991年4月.
[80] 万敏.大迎角定常/非定常气动力数值模拟.西北工业大学硕士学位论文.1999年3月.
[81] 肖志祥,李凤蔚,鄂秦.湍流模型在翼身组合体流场数值模拟中的应用研究.西北工业大学学报.Vol.21 No.1 2003.
[82] 李凤蔚,肖志祥.三种湍流模型模拟能力的对比.西北工业大学学报.Vol.20 No.3 2002
[83] Yang X. D., Ma H. Y. and Huang Y. N., "Prediction of Homogeneous Shear Flow and a Backward-Facing Step Flow with Some Linear and Non-linear K-ε Turbulence Models", Communication in Nonlinear Sciences and Numerical Simulation. November 2003
[84] David Degani, Lewis B. Schiff, "Computation of Turbulent Supersonic Flows around Pointed Bodies Having Crossflow Separation", Journal of Computational Physics 66, 173-196(1986)
[85] 杨云军,崔尔杰,周伟江.细长体大迎角非对称涡流数值模拟及形成机理的探讨.空气动力学会议论文集.中国宇航出版社.2003年10月
[86] 许洲.第四代战斗机空战仿真系统研究.西北工业大学博士学位论文.2001年.
[87] 蔡金狮.动力学系统辨识与建模.国防工业出版社,1991
[88] Yigang Fan and Frederick H. Lutze. Identification of an Unsteady Aerodynamic Model at High Angles of Attack. AIAA-96-3407-CP
[89] 焦天峰.大迎角非定常气动力数学模型研究.西北工业大学硕士学位论文.2000年3月.
[90] 陆璇.数理统计基础.清华大学出版社,1998.
[91] 张成乾,张国强.系统辨识与参数估计.机械工业出版社,1986