纵列式直升机双旋翼气动干扰特性的理论与试验研究
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摘要
本文建立了一套适合于悬停和前飞状态纵列式直升机双旋翼气动干扰特性计算的自由尾迹分析方法。利用该方法针对纵列式双旋翼和传统单旋翼的尾迹和气动特性进行了计算和分析。同时,使用模型旋翼台和风洞开展了纵列式直升机双旋翼气动干扰的试验研究。主要工作如下:作为前提和背景,本文首先对直升机旋翼自由尾迹方法研究、纵列式双旋翼气动干扰特性理论和试验研究的国内外现状进行了概述和分析,指出了现有研究中存在的不足,提出了本文拟采用的研究方法和研究内容。
在第二章,针对纵列式双旋翼涡尾迹主控方程的特点,引入了直线法将涡线偏微分方程转换成常微分方程再行求解,以有效提高数值稳定性。基于直线法,推导建立了一个新的用于求解旋翼尾迹涡线主控方程的数值算法。
论文的第三章,将旋翼自由尾迹模型、桨叶气动力模型、桨叶挥舞运动模型以及双旋翼配平模型进行耦合求解,并计入桨叶气流分离和压缩性的影响以及考虑大迎角时的气动力修正,发展了一套用于纵列式双旋翼气动干扰特性计算的迭代模型。然后,进行了悬停和前飞状态单旋翼和双旋翼的诱导速度、桨叶载荷和旋翼性能的算例计算,并与可得到的试验结果进行对比,验证了本文计算方法和程序的有效性。
第四章基于本文建立的模型和方法,计算了悬停和前飞状态纵列式双旋翼的尾迹结构、诱导速度分布及旋翼流场特性,着重讨论了纵列式双旋翼重叠区域和非重叠区域的尾迹和流场的不同特点。在此基础上,得出了一些新的结论。
在第五章,对悬停和前飞状态下纵列式双旋翼及单旋翼的桨叶气动载荷及旋翼性能进行了计算对比分析。定义了双旋翼拉力和功率干扰系数以及双旋翼附加功率因子,并以此为参数,较系统地研究了悬停和前飞状态双旋翼不同结构布局时的旋翼性能变化规律。得出了对纵列式双旋翼直升机结构布局设计有指导意义的结果。
本文第六章基于PIV技术,着重对纵列式模型双旋翼干扰状态下的后旋翼桨尖涡位移、涡核耗散特性、尾迹边界进行了试验研究。通过改变前后旋翼的水平和轴向间距、调整两旋翼之间的重叠区域大小研究了旋翼之间的相互干扰及对桨尖涡特性的影响。同时,还对比研究了单旋翼和双旋翼不同总距时旋翼桨尖涡涡核半径随涡龄角的变化规律。并将涡尾迹边界试验结果与本文算例的计算结果进行了比较。
第七章在南京航空航天大学重点实验室风洞中以及自行改装的纵列式双旋翼模型旋翼台上,针对悬停和前飞状态下的纵列式双旋翼流场速度特性和旋翼性能开展了试验研究。给出了纵列式双旋翼和单旋翼情况时的平均速度场、瞬态速度场及涡量分布的结果,以及纵列式旋翼性能随不同结构布局参数的变化。同时,应用先前章节发展的计算方法,针对所进行的单旋翼和双旋翼典型试验状态时的旋翼流场、旋翼性能进行了计算,并与试验结果进行了对比。
In this thesis, an iterative free-wake computational method has been developed for the prediction of aerodynamic interactional characteristics between the twin rotors of a tandem helicopter both in hover and in forward flight. By using this method, the calculations and analyses are given on the rotor wake and aerodynamic characteristics of a tandem twin-rotor and a single rotor. Meanwhile, the experiments on the aerodynamic interaction of the tandem twin rotors have been performed by using the model rotor test rig and wind tunnel. The major contributions of the author’s research work are as follows:
As the background of present work, the objectives of the research are described in the first chapter. The investigations and developments in the field of helicopter rotor free-wake research as well as the theoretical and experimental researches on the aerodynamic interaction of the tandem twin-rotor are introduced. The difficulties in the current research on the interactional aerodynamics of a tandem helicopter are pointed out. Also, the methods used in the present research are briefly introduced.
In Chapter 2, according to the feature of vortex governing equations for a tandem rotor, the Method of Line (MOL) is adopted to help change the vortex partial differential equations into the ordinary differential equations in order to improve the solution stability. Based on the MOL, a new numerical algorithm is derived to solve the rotor vortex governing equations. A free-wake computational method is established for a tandem rotor in Chapter 3, based on the MOL in Chapter 2. In this chapter, an iterative computational method has been developed for the prediction of aerodynamic interaction characteristics on the twin rotors of a tandem helicopter. In this method, the rotor free wake model, blade aerodynamic model, blade flap equations and twin-rotor trim model are coupled, and the effects of flow separation and compressibility are also included. Moreover, the aerodynamic correction at the large angle-of-attack condition is considered. Then, the induced-velocity distribution, the blade aerodynamic loading, and rotor performance on a tandem twin-rotor are calculated for both hover and forward flight, and the comparisons with the available experimental data are also made to show the capability of the present method.
In Chapter 4, by the method developed, rotor wake geometries, induced velocities, flow field characteristics of tandem rotors both in hover and in forward flight are calculated, the differences of rotor wake geometries and flow field between overlapping and un-overlapping area are discussed emphatically. On the basis of the above investigation, some new conclusions are obtained.
In Chapter 5, calculations and comparisons of the blade aerodynamic loading and rotor performance between a single rotor and a tandem rotor for both hover and forward flight are carried out. A set of Interaction Factors for twin rotors and Additional Power Factor for the interaction are defined. Based on the factors defined, the effects of such parameters as the longitudinal separation and axial separation between twin rotors on the rotor thrust and power are analyzed. As a result, some meaningful conclusions are obtained.
By the PIV technique, experimental investigations on the rotor blade tip vortices, vortex core dissipation and wake boundary for a tandem rotor model at the condition of interactions are studied in Chapter 6. The interactions between the twin rotors and their influences on blade tip vortices are discussed by altering the longitudinal and axial distances between twin rotors and thus changing the overlapping area. Meanwhile, the variations of vortex core radius with wake age for the single-rotor and dual-rotor at different blade collective-pitch angles are studied. In addition, the comparisons between experimental and calculated results by the present method on wake boundary are also made.
In Chapter 7, experimental investigations on the rotor flow fields and rotor performance of a tandem twin-rotor both in hover and in forward flight are carried out on the re-built tandem rotor model rig in the wind tunnel at the Nanjing University of Aeronautics and Astronautics. The results of the average wake velocity field, transient velocity field and vorticity distribution both for a tandem rotor and a single rotor are obtained. And the rotor performance variations with such parameters as the longitudinal separation and axial separation between twin rotors are also given. At the meantime, by applying the method developed in the previous chapters, computations of rotor flow field and rotor performance for a single rotor and a tandem rotor at typical measured conditions are performed, and then the computational results are compared with the present experimental data.
在第二章,针对纵列式双旋翼涡尾迹主控方程的特点,引入了直线法将涡线偏微分方程转换成常微分方程再行求解,以有效提高数值稳定性。基于直线法,推导建立了一个新的用于求解旋翼尾迹涡线主控方程的数值算法。
论文的第三章,将旋翼自由尾迹模型、桨叶气动力模型、桨叶挥舞运动模型以及双旋翼配平模型进行耦合求解,并计入桨叶气流分离和压缩性的影响以及考虑大迎角时的气动力修正,发展了一套用于纵列式双旋翼气动干扰特性计算的迭代模型。然后,进行了悬停和前飞状态单旋翼和双旋翼的诱导速度、桨叶载荷和旋翼性能的算例计算,并与可得到的试验结果进行对比,验证了本文计算方法和程序的有效性。
第四章基于本文建立的模型和方法,计算了悬停和前飞状态纵列式双旋翼的尾迹结构、诱导速度分布及旋翼流场特性,着重讨论了纵列式双旋翼重叠区域和非重叠区域的尾迹和流场的不同特点。在此基础上,得出了一些新的结论。
在第五章,对悬停和前飞状态下纵列式双旋翼及单旋翼的桨叶气动载荷及旋翼性能进行了计算对比分析。定义了双旋翼拉力和功率干扰系数以及双旋翼附加功率因子,并以此为参数,较系统地研究了悬停和前飞状态双旋翼不同结构布局时的旋翼性能变化规律。得出了对纵列式双旋翼直升机结构布局设计有指导意义的结果。
本文第六章基于PIV技术,着重对纵列式模型双旋翼干扰状态下的后旋翼桨尖涡位移、涡核耗散特性、尾迹边界进行了试验研究。通过改变前后旋翼的水平和轴向间距、调整两旋翼之间的重叠区域大小研究了旋翼之间的相互干扰及对桨尖涡特性的影响。同时,还对比研究了单旋翼和双旋翼不同总距时旋翼桨尖涡涡核半径随涡龄角的变化规律。并将涡尾迹边界试验结果与本文算例的计算结果进行了比较。
第七章在南京航空航天大学重点实验室风洞中以及自行改装的纵列式双旋翼模型旋翼台上,针对悬停和前飞状态下的纵列式双旋翼流场速度特性和旋翼性能开展了试验研究。给出了纵列式双旋翼和单旋翼情况时的平均速度场、瞬态速度场及涡量分布的结果,以及纵列式旋翼性能随不同结构布局参数的变化。同时,应用先前章节发展的计算方法,针对所进行的单旋翼和双旋翼典型试验状态时的旋翼流场、旋翼性能进行了计算,并与试验结果进行了对比。
In this thesis, an iterative free-wake computational method has been developed for the prediction of aerodynamic interactional characteristics between the twin rotors of a tandem helicopter both in hover and in forward flight. By using this method, the calculations and analyses are given on the rotor wake and aerodynamic characteristics of a tandem twin-rotor and a single rotor. Meanwhile, the experiments on the aerodynamic interaction of the tandem twin rotors have been performed by using the model rotor test rig and wind tunnel. The major contributions of the author’s research work are as follows:
As the background of present work, the objectives of the research are described in the first chapter. The investigations and developments in the field of helicopter rotor free-wake research as well as the theoretical and experimental researches on the aerodynamic interaction of the tandem twin-rotor are introduced. The difficulties in the current research on the interactional aerodynamics of a tandem helicopter are pointed out. Also, the methods used in the present research are briefly introduced.
In Chapter 2, according to the feature of vortex governing equations for a tandem rotor, the Method of Line (MOL) is adopted to help change the vortex partial differential equations into the ordinary differential equations in order to improve the solution stability. Based on the MOL, a new numerical algorithm is derived to solve the rotor vortex governing equations. A free-wake computational method is established for a tandem rotor in Chapter 3, based on the MOL in Chapter 2. In this chapter, an iterative computational method has been developed for the prediction of aerodynamic interaction characteristics on the twin rotors of a tandem helicopter. In this method, the rotor free wake model, blade aerodynamic model, blade flap equations and twin-rotor trim model are coupled, and the effects of flow separation and compressibility are also included. Moreover, the aerodynamic correction at the large angle-of-attack condition is considered. Then, the induced-velocity distribution, the blade aerodynamic loading, and rotor performance on a tandem twin-rotor are calculated for both hover and forward flight, and the comparisons with the available experimental data are also made to show the capability of the present method.
In Chapter 4, by the method developed, rotor wake geometries, induced velocities, flow field characteristics of tandem rotors both in hover and in forward flight are calculated, the differences of rotor wake geometries and flow field between overlapping and un-overlapping area are discussed emphatically. On the basis of the above investigation, some new conclusions are obtained.
In Chapter 5, calculations and comparisons of the blade aerodynamic loading and rotor performance between a single rotor and a tandem rotor for both hover and forward flight are carried out. A set of Interaction Factors for twin rotors and Additional Power Factor for the interaction are defined. Based on the factors defined, the effects of such parameters as the longitudinal separation and axial separation between twin rotors on the rotor thrust and power are analyzed. As a result, some meaningful conclusions are obtained.
By the PIV technique, experimental investigations on the rotor blade tip vortices, vortex core dissipation and wake boundary for a tandem rotor model at the condition of interactions are studied in Chapter 6. The interactions between the twin rotors and their influences on blade tip vortices are discussed by altering the longitudinal and axial distances between twin rotors and thus changing the overlapping area. Meanwhile, the variations of vortex core radius with wake age for the single-rotor and dual-rotor at different blade collective-pitch angles are studied. In addition, the comparisons between experimental and calculated results by the present method on wake boundary are also made.
In Chapter 7, experimental investigations on the rotor flow fields and rotor performance of a tandem twin-rotor both in hover and in forward flight are carried out on the re-built tandem rotor model rig in the wind tunnel at the Nanjing University of Aeronautics and Astronautics. The results of the average wake velocity field, transient velocity field and vorticity distribution both for a tandem rotor and a single rotor are obtained. And the rotor performance variations with such parameters as the longitudinal separation and axial separation between twin rotors are also given. At the meantime, by applying the method developed in the previous chapters, computations of rotor flow field and rotor performance for a single rotor and a tandem rotor at typical measured conditions are performed, and then the computational results are compared with the present experimental data.
引文
[1] Johnson W. Helicopter Theory, Princeton University Press, 1980.
[2] Egolf, T. A., Landgrebe, A. J., Helicopter Rotor Wake Geometry and Its Influence in Forward Flight. NASA CR-3726, 1983.
[3] Martin P. B. et al., High Resolution Trailing Vortex Measurements in the Wake of a Hovering Rotor. Proceedings of the American Helicopter Society 57th Annual National Forum, 2001.
[4] Kang H. J., Kwon O. J., Unstructured Mesh Navier-Stokes Calculations of the Flowfield of a Helicopter in Hover. Journal of the American Helicopter Society, 2002, 47(2):90~99.
[5] Park Y. M., Kwon O. J., Simulation of Unsteady Rotor Flow Field Using Unstructured Adaptive Sliding Meshes. Journal of the American Helicopter Society, 2004, 49(4): 391-400.
[6] Lakshminarayan V., Baeder J. D., Computational Investigation of Small Scale Coaxial Rotor Aerodynamics in Hover. AIAA 2009-1069, 2009
[7] Kumar M., Murthy V. R., Efficient Rotor Flow Calculation Using Multi-Blade Coordinate Transfromed CFD in Frequency Domain. AIAA 2008-408, 2008
[8]许和勇,叶正寅,王刚等.基于非结构运动对接网格的旋翼前飞流场数值模拟.空气动力学学报.2007, 25(3):325~329.
[9]宋文萍,韩忠华,王立群等.旋翼桨尖几何形状对旋翼气动噪声影响的定量计算分析.计算物理.2001, 18(6):569~572.
[10]韩忠华,宋文萍,乔志德.基于FW-H方程的旋翼气动声学计算研究.航空学报.2003, 24(5): 400~404
[11] Zhao Qijun, Xu Guohua, Zhao Jinggen, Numerical Simulations of the Unsteady Flowfield of Helicopter Rotors on Moving Embedded Grids, Aerospace Science and Technology, 2005,9(2):117~124
[12] Clark D R, Leiper A C, The free wake analysis: A Method for Prediction of Helicopter Rotor Hovering Performance, Journal of the American Helicopter Society, 1970, 15(1):3~11.
[13] Landgrebe A J, An Analytical Method for Predicting Rotor Wake Geometry, Presented at the AIAA/AHS VTOL Research, Design & Operations Meeting, 1969.
[14] Landgrebe A J, the Wake Geometry of a Hovering Rotor and its Influence on Rotor Performance, Journal of the American Helicopter Society, 1972, 17(4):2~15.
[15] Landgrebe A.J., Prediction of Helicopter Induced Flow Velocities Using the Rotorcraft WakeAnanlysis, Presented at the 32nd Annual Forum of the American Helicopter Society, 1976.
[16] Sadler S G, A Method for Predicting Helicopter Wake Geometry, Wake-Induced Inflow and Wake Effects on Blade Airloads, Proceedings of the American Helicopter Society 27th Annual Forum, 1971.
[17] Scully M P, Computation of Helicopter Rotor Wake Geometry and Its Influence on Rotor Harmonic Airloads, Massachusetts Institute of Technology, ASRL TR 178-1,1975.
[18] Scully M. P.: A Method of Computing Helicopter Vortex Wake Distortion, Massachusetts Institute of Technology, ASRL TR-138-1, 1967.
[19] Johnson W A, Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dynamics, Part I: Analytical Development, NASA TM 81182, 1980.
[20] Johnson W., Airloads and Wake Models for a Comprehensive Helicopter Analysis, Vertica, 1990, 14(03), 22~35.
[21] Johnson W, A General Free Wake Geometry Calculation for Wings and Rotors, Proceedings of the American Helicopter Society 51st Annual Forum, 1995.
[22] Miller R H, A Simplified Approach to the Free Wake Analysis of a Hovering Rotor, Vertica, 1982, 6(1):89~95.
[23] Miller R. H.: A Simplified Approach to the Free Wake Analysis of a Hovering Rotor, Presented at the 7th European Rotorcraft Forum, 1981.
[24] Weissinger J, the Lift Distribution of Swept-Back Wings, NACA TM 1120, 1947.
[25] Bliss D B, Washspress D A, Quackenbush T R, A New Approach to the Free Wake Problem for Hovering Rotors, Proceedings of the American Helicopter Society 41st Annual Forum, 1985.
[26] Egolf T A, Massar J P, Helicopter Free Wake Implementation on Advanced Computer Architecture, Proceedings of the 2nd International Conference on Rotorcraft Basis Research, 1988.
[27] Egolf T A, Rotor Wake Modeling for High Speed Applications, Proceedings of the American Helicopter Society 44th Annual Forum, 1988.
[28] Miller W O, A Fast Adaptive Resolution Method for Efficient Free Wake Calculations, Proceedings of the American Helicopter Society 49th Annual National Forum, 1993.
[29] Miller W.O., Bliss D.B.: Direct Period Solutions of Rotor Free Wake Calculations, Journal of the American Helicopter Society, 1993, 38(2):53~60.
[30] Bagai A, Leishman J G, Rotor Free-Wake Modeling Using a Pseudo-Implicit Algorithm. Journal of Aircraft, 1995, 32(6):1276~1285.
[31] Bagai A., Leishman J.G., Free-Wake Analysis of Tandem, Tilt-Rotor and Coaxial RotorConfigurations, Presented at the 51st Annual Forum of the American Helicopter Society, 1995
[32] Wachspress D.A., Quackenbush T.R.: First Principles Free Vortex Wake Analysis for Helicopters and Tiltrotors, Presented at the 59th Annual Forum of the American Helicopter Society, 2003.
[33] Allin G.A., Brown R.E.: Investigating the Physics of the Vortex Ring State Using the Vorticity Transport Model, Presented at the 31st European Rotorcraft Forum, 2005.
[34]徐国华,王适存.悬停旋翼的自由尾迹计算.南京航空航天大学学报.1998,30(2):126~131.
[35] Xu G. H., Wang S. C., Zhao J. G., Experimental and Analytical Investigation on Aerodynamic Characteristics of Helicopter Scissors Tail Rotor. Chinese Journal of Aeronautics, 2001, 14(4): 193~199.
[36]曹义华.旋翼涡尾流与下洗流场的计算方法.北京航空航天大学学报.2000,26(2):174~177
[37]孙茂.直升机机身对旋翼的干扰.航空学报.1988, 9(3):108~112.
[38]楼武疆.旋翼尾迹描述新法及其计算.博士学位论文.南京航空航天大学, 1990.
[39]徐国华,使用自由尾迹分析的新型桨尖旋翼气动特性研究,博士学位论文,南京航空航天大学, 1996.
[40]徐国华,王适存.前飞状态直升机旋翼的自由尾迹计算.南京航空航天大学学报.1997, 29(6):648~653.
[41]赵景根,高正,徐国华.直升机旋翼/机身气动干扰的计算方法.南京航空航天大学学报.2000, 32(4):369~374.
[42]曾洪江,胡继忠.一种新的自由涡尾迹计算方法.航空学报.2004, 25(6):546~550.
[43]黄水林,李春华,徐国华.基于自由尾迹和升力面方法的双旋翼悬停气动干扰计算.空气动力学学报.2007,25(3):390~395
[44]李春华.时间准确自由尾迹方法建模及(倾转)旋翼气动特性分析.博士学位论文.南京航空航天大学, 2007.
[45] Celi R., State-Space Representation of Vortex Wakes Using the Method of Lines, Proceedings of 30th European Rotorcraft Forum, 2004.
[46] Ma, J.G. and Chen, Z., Application of the Method of Lines to the Laplace Equation, Micro. Opt. tech, Lett. ,1997,14(6),330~333
[47] Tanner W. H.: Charts for Estimating Rotary Wing Performance in Hover and at High Forward Speeds, NASA CR-114, 1964.
[48] Kocurek J. D., Tangler J. L.: A Prescribed Wake Lifting Surface Hover Performance Analysis, Journal of American Helicopter Society, 1977, 22(01): 24~35.
[49] Quackenbush T. R., Bliss D. B., Wachspress D. A., Ong C. C.,Free Wake Analysis of HoverPerformance Using a New Influence Coefficient Method, NASA CR-4309, 1990.
[50] Quackenbush T. R., et al., Optimization of Rotor Performance in Hover Using a Free Wake Analysis,Journal of Aircraft, 1991, 28(3):200~207.
[51] Quackenbush T.R., Boschitsch A.H., Wachspress D.A., et al, Rotor Design Optimization Using a Free Wake Analysis, NASA-CR-177612, 1993.
[52] Satio S.and Azuma A., A Numerical Approach to Coaxial Rotor Aerodynamics, Vertica, 1982, 6(2):253~266.
[53] Andrew M. J., Coaxial Rotor Aerodynamics in Hover, Vetica, 1981, 5(2):163~172.
[54] Glusman S T, Hyland R A, Marr R L, V-22 Technical Challenges, Presented at the AGARD Advances in Rotorcraft Technologies Symposium, 1996.
[55] Felker F, Results from a Test of a 2/3-scale V-22 Rotor and Wing in the 40-by 80- Foot Wind Tunnel, Proceedings of the American Helicopter society 47th Anuual Forum, 1991.
[56] Stepniewski, W. Z., Key, C.N., Rotorary Wing Aerodynamics, Dover Publications, 1984.
[57] Harris F.D., Twin Rotor Hover Performance. Journal of the American helicopter society, 1999.44(1):34~37
[58] Leishman J G, Bhagwat M J, Ananthan S, Free-vortex Wake Predictions of the Vortex Ring State for Single-rotor and Multi-rotor Configuration. Proceedings of the American Helicopter Society 58th Annual Forum, 2002.
[59] Griffiths D.A., Leishman J.G., A Study of Dual-rotor Interference and Ground Effect using a Free-vortex Wake Model, Presented at the 58th Annual Forum of the AHS, 2002.
[60] Landgrebe A J. An Analytical and Experimental Investigation of Helicopter Rotor Hover Performance and Wake Geometry Characteristics, USAAMRDL TR 71-24, 1971
[61] Heineck J T et al. Application of Three-Component PIV to A Hovering Rotor Wake, Proceedings of the American Helicopter Society Annual Forum, 2000.
[62] Martin P B et al. Visualization of a Helicopter Rotor Wake in Hover. AIAA 9923225,1999.
[63] Scheiman J. A Tabulation of Helicopter Rotor-Blade Differential Pressures, Stress and Motions Measured in Flight. NASA TM-X952, 1974.
[64] P. F. Lorber, R. C. Stauter, A. J. Landgrebe, A Comprehensive Hover Test of the Airloads and Airflow of an Extensively Instrumented Model Helicopter Rotor, Proceedings of the American Helicopter Society 45th Forum, 1989
[65] William T., Matthew L.: Loads and Performance Data from a Wind-Tunnel Test of Generic Model Helicopter Rotor Blades, NASA-TP-213937, 2005.
[66] Althoff S. L., Effect of Advanced Rotorcraft Airfoil Sections on the Hover Performance of aSmall-Scale Rotor Model, NASA-TP-2832, 1988.
[67] Shinoda P. M., Johnson W., Performance Results from a Test of an S-76 Rotor in the NASA Ames 80-by 120-Foot Wind Tunnel, AIAA-93-3414-CP, 1993.
[68] Coleman C.P., A Survey of Theoretical And Experimental Coaxial Rotor Aerodynamic Research, Presented at the 19th European Rotorcraft Forum, 1993.
[69] Akmov A. I., Butov V P., Bourtsev B N. , Selemenev S.V. , Flight Investigation of Coaxial Rotor Tip Vortex Structure,Presented at the American Helicopter Society 50th Annual Forum, 1994
[70] Mcveigh M. A., the V-22 Tilit-Rotor Large-Scale Rotor Performance/Wing Download Test and Comparison with Theory, Vertica, 1986, 10(3): 281~297.
[71] Felker F. F., et al. Performance and Loads Data from a Hover Test of a 0.658-scale V-22 Rotor and Wind, NASA-TM-89419, 1987
[72] Dingeldein R C. Wind-tunnel Studies of Performance of Multi-Rotor Configurations. National Advisory Committee for Aeronautics, NACA TN 3236, 1954.
[73] Pruyn R R and Alexander W T. The USAavlabs Tandem Rotor Air Loads Measurement Program. Proceedings of the Aerodynamics Testing Conference, 1966.
[74] Huston R J. Wind Tunnel Measurements of Performance, Blade Motions, and Blade Airlords for Tandem-Rotor Configurations with and Without Overlap. National Aeronautics and Space Administration, NASA TN D-1971, 1963.
[75]徐国华,王适存.具有后掠桨尖的旋翼气动特性计算方法.空气动力学学报.1999, 17(03): 356~361.
[76] Xu, G.H. and Newman, S.J. A Full-Span Free-Wake Model Using Circular-Arc Vortex Elements and Incorporating Rotor Trim Analysis.Journal of Aerospace Engineering, 2006, 220(2):145-163.
[77] Xu G.H., Zhao Q. J., Gao Z., et al, Prediction of Aerodynamics Interactions of Helicopter Rotor on Its Fuselage, Chinese Journal of Aeronautics, 2002, 15(01): 12~17.
[78]童自力,孙茂.纵列式及横列式双旋翼流动的N-S方程模拟及气动特性的研究.航空学报,1999, 20(6):489~492.
[79]王平,王适存等.共轴式双旋翼气动特性分析及实验研究.第13届全国直升机年会论文集.1997.
[80]陈铭,胡继忠,曹义华.共轴双旋翼前飞气动特性固定尾迹分析.2004,30(1):74~78.
[81]李春华,徐国华.悬停和前飞状态倾转旋翼自由尾迹分析,空气动力学学报.2005,23(2):152~156
[82]黄水林,徐国华,招启军.纵列式直升机双旋翼流场特性的自由尾迹分析,空气动力学学报.2008.12,26(4): 473~479.
[83]李攀,张学军,陈仁良,双旋翼系统自由尾迹分析,第20届全国直升机年会论文集,2004
[84]唐正飞,李锋,高正,梅卫胜,用三维激光多谱勒测速仪对共轴双旋翼悬停流场的测定,流体力学实验与测量, 1998,12(1),81~87.
[85]邓彦敏等.共轴式直升上下旋翼之间气动干扰的风洞实验研究,航空学报, 2003,24(1),10~14
[86] Zili T., Mao S., Flow Analysis of Twin-Rotor Configurations by Navier-Strokes Simulation. Journal of the American Helicopter Society, 2000.45(2):97~105.
[87] Daminlig C B, and Edward T M. Computational modeling of the CH-47 helicopter in hover. Proceedings of the 2007 DoD High Performance Computing Modernization Program Users Group Conference, IEEE Computer Society, 2007, 98~103.
[88]吴林波:纵列式直升机双旋翼机身流场特性的CFD分析,硕士学位论文,南京,南京航空航天大学,2009.
[89] Leishman J G, Bagai A, Free-Wake Analysis of Twin-Rotor Systems, Proceedings of the 20th European Rotorcraft Forum, 1994.
[90] Bagai A, Leishman J G, Park J., Aerodynamic Analysis of A Helicopter in Steady Maneuvering Flight using a Free-Vortex Rotor Wake Model. Journal of the American Helicopter Society, 1999.
[91] He, C.J., Development and Application of a Generalized Dynamic Wake Theory for Lifting Rotors, Ph.D. thesis, Georgia Institute of Technology, Georgia, 1989.
[92] Leishman, J. G., Principles of Helicopter Aerodynamics, Cambridge University Press, New York, 2000.
[93] Bhagwat M J, Transient Dynamics of Helicopter Rotor Wakes Using a Time-accurate Free-vortex Method, PhD thesis, University of Maryland, Maryland,2001.
[94]赵景根:直升机旋翼/机身气动干扰的研究,硕士学位论文,南京航空航天大学,南京,2001.
[95]胡健伟、汤怀民,微分方程数值方法,科学出版社,2003.
[96] Carver, M. B., and Hinds, H. W., the Method of Lines and the Advection Equation, Simulation, Vol., 1978, 31(2):59~69.
[97] Schiesser, W. E., the Numerical Method of Lines: Integration of Partial Differential Equations, Academic Press, San Diego, 1991.
[98]关治、陆金甫,数值分析基础,高等教育出版社,2005.
[99] M. N. O. Sadiku and C. N. Obiozor, a Simple Introduction to the Method of Lines,International Journal of Electrical Engineering Education, 2000, 282~296.
[100] Bhagwat M J, Leishman J G, Correlation of Helicopter Tip Vortex Measurements, AIAA Journal, 2000, 38(2):301~308.
[101] Vatistas G H, New Model for Intense Self-Similar Vortices, Journal of Propulsion and Power, 1998, 14(4): 462~469.
[102] Vatistas G H, Kozel V, Mih W C, A Simpler Model for Concentrated Vortices, Experiments in Fluids, 1991, 11:73~76.
[103] Bhagwat M J, Transient Dynamics of Helicopter Rotor Wakes Using a Time-accurate Free-vortex Method, PhD thesis, University of Maryland, 2001.
[104] Bagai A, Contributions to the Mathematical Modeling of Rotor Flow-Fields using a Pseudo-Implicit Free-Wake Analysis, PhD thesis, University of Maryland, Maryland,1995.
[105] Lorber P. F., Stauter R. C., Landgrebe A. J., A Comprehensive Hover Test of the Airloads and Airflow of an Extensively Instrumented Model Helicopter Rotor. Proceedings of the American Helicopter Society 45th Annual Forum, 1989.
[106] Petot, D., Stall Effects and Blade Torsion-An Evaluation of Predictive Tools, Journal of the American Helicopter Society, 1999, 44(4):320~331.
[107] Beddoes T S, Representation of Airfoil Behavior, Vertica, 1983, 7(2):183~197.
[108] Leishman, J.G.., Validation of Approximate Indicial Aerodynamic Functions for Two-Dimensional Subsonic Flow. Journal of Aircraft, 1988, 25(10):510~521.
[109] Leishman, J.G., and Nguyen, K.Q. State-Space Representation of Unsteady Airfoil Behavior. AIAA Journal, 1990, 28(5):20~28.
[110] Thwaites B, Incompressible Aerodynamics, Oxford Univ. Press, Oxford, UK, 1960.
[111] Xu Guohua, Newman S J., Helicopter Rotor Free Wake Calculations Using a New Relaxation Technique,the 26th European Rotorcraft Forum, Netherlands,2000
[112] Leishman, J.G., Bagai A. Fundamental Studies of Rotor Wakes in Low Speed Forward Flight Using Wide-Field Shadowgraphy. Proceedings of AIAA 9th Applied Aerodynamics Meeting, 1991.
[113]王适存主编,直升机空气动力学,航空专业教材编审组,1983.
[114] Lorber P. F. and Egolf T. A., an Unsteady Helicopter Rotor-Fuselage Aerodynamic Interaction Analysis, Journal of the American Helicopter Society, 1990, 35(3):120~128.
[115] Leishman J.G. and Bi N.P., Measurement of a Rotor Flowfield and the Effects on a Fuselage in Forward Flight, Vertica, 1990. 14(3), 401~415.
[116] Leishman J.G., Bi N.P.and D.K. etc., Investigation of Aerodynamic Interactions Between a Rotor and a Fuselage in Forward Flight, Presented at the 45th Annual Forum of the AmericanHelicopter Society, Boston, MA, May 1989, 591~601.
[117] Bagai, A., Leishman, J. G., Rotor Free Wake Modeling Using Relaxation Technique-Including Comparisons with Experimental Data. Journal of the American Helicopter Society, 1995, 40(3):122~129.
[118] R.W.普罗蒂,直升机性能及稳定性和操作性,高正等译,航空工业出版社,1990.
[119]郭才根,郭士龙,直升机总体设计,航空工业出版社,1993.
[120] Tangler, J. L., Wohlfeld, R. M., and Miley, S. J., An Experimental Investigation of Vortex Stability, Tip Shapes, Compressibility, and Noise for Hovering Model Rotors, NASA CR-2305, 1973.
[121] Leishman, J. G., Baker, A., and Coyne, A., Measurements of Rotor Tip Vortices Using Three-Component Laser Doppler Velocimetry, Journal of the American Helicopter Society, , 1996, 41(4) 342~353.
[122] Martin, P. B., Pugliese, G. J. and Leishman, J. G., Stereoscopic PIV Measurements in the Wake of a Hovering Rotor, Proceedings of the American Helicopter Society 56th Annual Forum, 2000.
[123] Bhagwat, M. J., and Leishman, J. G., Stability Analysis of Helicopter Rotor Wakes in Axial Flight, Journal of the American Helicopter Society, 2000, 45(2),165~178
[2] Egolf, T. A., Landgrebe, A. J., Helicopter Rotor Wake Geometry and Its Influence in Forward Flight. NASA CR-3726, 1983.
[3] Martin P. B. et al., High Resolution Trailing Vortex Measurements in the Wake of a Hovering Rotor. Proceedings of the American Helicopter Society 57th Annual National Forum, 2001.
[4] Kang H. J., Kwon O. J., Unstructured Mesh Navier-Stokes Calculations of the Flowfield of a Helicopter in Hover. Journal of the American Helicopter Society, 2002, 47(2):90~99.
[5] Park Y. M., Kwon O. J., Simulation of Unsteady Rotor Flow Field Using Unstructured Adaptive Sliding Meshes. Journal of the American Helicopter Society, 2004, 49(4): 391-400.
[6] Lakshminarayan V., Baeder J. D., Computational Investigation of Small Scale Coaxial Rotor Aerodynamics in Hover. AIAA 2009-1069, 2009
[7] Kumar M., Murthy V. R., Efficient Rotor Flow Calculation Using Multi-Blade Coordinate Transfromed CFD in Frequency Domain. AIAA 2008-408, 2008
[8]许和勇,叶正寅,王刚等.基于非结构运动对接网格的旋翼前飞流场数值模拟.空气动力学学报.2007, 25(3):325~329.
[9]宋文萍,韩忠华,王立群等.旋翼桨尖几何形状对旋翼气动噪声影响的定量计算分析.计算物理.2001, 18(6):569~572.
[10]韩忠华,宋文萍,乔志德.基于FW-H方程的旋翼气动声学计算研究.航空学报.2003, 24(5): 400~404
[11] Zhao Qijun, Xu Guohua, Zhao Jinggen, Numerical Simulations of the Unsteady Flowfield of Helicopter Rotors on Moving Embedded Grids, Aerospace Science and Technology, 2005,9(2):117~124
[12] Clark D R, Leiper A C, The free wake analysis: A Method for Prediction of Helicopter Rotor Hovering Performance, Journal of the American Helicopter Society, 1970, 15(1):3~11.
[13] Landgrebe A J, An Analytical Method for Predicting Rotor Wake Geometry, Presented at the AIAA/AHS VTOL Research, Design & Operations Meeting, 1969.
[14] Landgrebe A J, the Wake Geometry of a Hovering Rotor and its Influence on Rotor Performance, Journal of the American Helicopter Society, 1972, 17(4):2~15.
[15] Landgrebe A.J., Prediction of Helicopter Induced Flow Velocities Using the Rotorcraft WakeAnanlysis, Presented at the 32nd Annual Forum of the American Helicopter Society, 1976.
[16] Sadler S G, A Method for Predicting Helicopter Wake Geometry, Wake-Induced Inflow and Wake Effects on Blade Airloads, Proceedings of the American Helicopter Society 27th Annual Forum, 1971.
[17] Scully M P, Computation of Helicopter Rotor Wake Geometry and Its Influence on Rotor Harmonic Airloads, Massachusetts Institute of Technology, ASRL TR 178-1,1975.
[18] Scully M. P.: A Method of Computing Helicopter Vortex Wake Distortion, Massachusetts Institute of Technology, ASRL TR-138-1, 1967.
[19] Johnson W A, Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dynamics, Part I: Analytical Development, NASA TM 81182, 1980.
[20] Johnson W., Airloads and Wake Models for a Comprehensive Helicopter Analysis, Vertica, 1990, 14(03), 22~35.
[21] Johnson W, A General Free Wake Geometry Calculation for Wings and Rotors, Proceedings of the American Helicopter Society 51st Annual Forum, 1995.
[22] Miller R H, A Simplified Approach to the Free Wake Analysis of a Hovering Rotor, Vertica, 1982, 6(1):89~95.
[23] Miller R. H.: A Simplified Approach to the Free Wake Analysis of a Hovering Rotor, Presented at the 7th European Rotorcraft Forum, 1981.
[24] Weissinger J, the Lift Distribution of Swept-Back Wings, NACA TM 1120, 1947.
[25] Bliss D B, Washspress D A, Quackenbush T R, A New Approach to the Free Wake Problem for Hovering Rotors, Proceedings of the American Helicopter Society 41st Annual Forum, 1985.
[26] Egolf T A, Massar J P, Helicopter Free Wake Implementation on Advanced Computer Architecture, Proceedings of the 2nd International Conference on Rotorcraft Basis Research, 1988.
[27] Egolf T A, Rotor Wake Modeling for High Speed Applications, Proceedings of the American Helicopter Society 44th Annual Forum, 1988.
[28] Miller W O, A Fast Adaptive Resolution Method for Efficient Free Wake Calculations, Proceedings of the American Helicopter Society 49th Annual National Forum, 1993.
[29] Miller W.O., Bliss D.B.: Direct Period Solutions of Rotor Free Wake Calculations, Journal of the American Helicopter Society, 1993, 38(2):53~60.
[30] Bagai A, Leishman J G, Rotor Free-Wake Modeling Using a Pseudo-Implicit Algorithm. Journal of Aircraft, 1995, 32(6):1276~1285.
[31] Bagai A., Leishman J.G., Free-Wake Analysis of Tandem, Tilt-Rotor and Coaxial RotorConfigurations, Presented at the 51st Annual Forum of the American Helicopter Society, 1995
[32] Wachspress D.A., Quackenbush T.R.: First Principles Free Vortex Wake Analysis for Helicopters and Tiltrotors, Presented at the 59th Annual Forum of the American Helicopter Society, 2003.
[33] Allin G.A., Brown R.E.: Investigating the Physics of the Vortex Ring State Using the Vorticity Transport Model, Presented at the 31st European Rotorcraft Forum, 2005.
[34]徐国华,王适存.悬停旋翼的自由尾迹计算.南京航空航天大学学报.1998,30(2):126~131.
[35] Xu G. H., Wang S. C., Zhao J. G., Experimental and Analytical Investigation on Aerodynamic Characteristics of Helicopter Scissors Tail Rotor. Chinese Journal of Aeronautics, 2001, 14(4): 193~199.
[36]曹义华.旋翼涡尾流与下洗流场的计算方法.北京航空航天大学学报.2000,26(2):174~177
[37]孙茂.直升机机身对旋翼的干扰.航空学报.1988, 9(3):108~112.
[38]楼武疆.旋翼尾迹描述新法及其计算.博士学位论文.南京航空航天大学, 1990.
[39]徐国华,使用自由尾迹分析的新型桨尖旋翼气动特性研究,博士学位论文,南京航空航天大学, 1996.
[40]徐国华,王适存.前飞状态直升机旋翼的自由尾迹计算.南京航空航天大学学报.1997, 29(6):648~653.
[41]赵景根,高正,徐国华.直升机旋翼/机身气动干扰的计算方法.南京航空航天大学学报.2000, 32(4):369~374.
[42]曾洪江,胡继忠.一种新的自由涡尾迹计算方法.航空学报.2004, 25(6):546~550.
[43]黄水林,李春华,徐国华.基于自由尾迹和升力面方法的双旋翼悬停气动干扰计算.空气动力学学报.2007,25(3):390~395
[44]李春华.时间准确自由尾迹方法建模及(倾转)旋翼气动特性分析.博士学位论文.南京航空航天大学, 2007.
[45] Celi R., State-Space Representation of Vortex Wakes Using the Method of Lines, Proceedings of 30th European Rotorcraft Forum, 2004.
[46] Ma, J.G. and Chen, Z., Application of the Method of Lines to the Laplace Equation, Micro. Opt. tech, Lett. ,1997,14(6),330~333
[47] Tanner W. H.: Charts for Estimating Rotary Wing Performance in Hover and at High Forward Speeds, NASA CR-114, 1964.
[48] Kocurek J. D., Tangler J. L.: A Prescribed Wake Lifting Surface Hover Performance Analysis, Journal of American Helicopter Society, 1977, 22(01): 24~35.
[49] Quackenbush T. R., Bliss D. B., Wachspress D. A., Ong C. C.,Free Wake Analysis of HoverPerformance Using a New Influence Coefficient Method, NASA CR-4309, 1990.
[50] Quackenbush T. R., et al., Optimization of Rotor Performance in Hover Using a Free Wake Analysis,Journal of Aircraft, 1991, 28(3):200~207.
[51] Quackenbush T.R., Boschitsch A.H., Wachspress D.A., et al, Rotor Design Optimization Using a Free Wake Analysis, NASA-CR-177612, 1993.
[52] Satio S.and Azuma A., A Numerical Approach to Coaxial Rotor Aerodynamics, Vertica, 1982, 6(2):253~266.
[53] Andrew M. J., Coaxial Rotor Aerodynamics in Hover, Vetica, 1981, 5(2):163~172.
[54] Glusman S T, Hyland R A, Marr R L, V-22 Technical Challenges, Presented at the AGARD Advances in Rotorcraft Technologies Symposium, 1996.
[55] Felker F, Results from a Test of a 2/3-scale V-22 Rotor and Wing in the 40-by 80- Foot Wind Tunnel, Proceedings of the American Helicopter society 47th Anuual Forum, 1991.
[56] Stepniewski, W. Z., Key, C.N., Rotorary Wing Aerodynamics, Dover Publications, 1984.
[57] Harris F.D., Twin Rotor Hover Performance. Journal of the American helicopter society, 1999.44(1):34~37
[58] Leishman J G, Bhagwat M J, Ananthan S, Free-vortex Wake Predictions of the Vortex Ring State for Single-rotor and Multi-rotor Configuration. Proceedings of the American Helicopter Society 58th Annual Forum, 2002.
[59] Griffiths D.A., Leishman J.G., A Study of Dual-rotor Interference and Ground Effect using a Free-vortex Wake Model, Presented at the 58th Annual Forum of the AHS, 2002.
[60] Landgrebe A J. An Analytical and Experimental Investigation of Helicopter Rotor Hover Performance and Wake Geometry Characteristics, USAAMRDL TR 71-24, 1971
[61] Heineck J T et al. Application of Three-Component PIV to A Hovering Rotor Wake, Proceedings of the American Helicopter Society Annual Forum, 2000.
[62] Martin P B et al. Visualization of a Helicopter Rotor Wake in Hover. AIAA 9923225,1999.
[63] Scheiman J. A Tabulation of Helicopter Rotor-Blade Differential Pressures, Stress and Motions Measured in Flight. NASA TM-X952, 1974.
[64] P. F. Lorber, R. C. Stauter, A. J. Landgrebe, A Comprehensive Hover Test of the Airloads and Airflow of an Extensively Instrumented Model Helicopter Rotor, Proceedings of the American Helicopter Society 45th Forum, 1989
[65] William T., Matthew L.: Loads and Performance Data from a Wind-Tunnel Test of Generic Model Helicopter Rotor Blades, NASA-TP-213937, 2005.
[66] Althoff S. L., Effect of Advanced Rotorcraft Airfoil Sections on the Hover Performance of aSmall-Scale Rotor Model, NASA-TP-2832, 1988.
[67] Shinoda P. M., Johnson W., Performance Results from a Test of an S-76 Rotor in the NASA Ames 80-by 120-Foot Wind Tunnel, AIAA-93-3414-CP, 1993.
[68] Coleman C.P., A Survey of Theoretical And Experimental Coaxial Rotor Aerodynamic Research, Presented at the 19th European Rotorcraft Forum, 1993.
[69] Akmov A. I., Butov V P., Bourtsev B N. , Selemenev S.V. , Flight Investigation of Coaxial Rotor Tip Vortex Structure,Presented at the American Helicopter Society 50th Annual Forum, 1994
[70] Mcveigh M. A., the V-22 Tilit-Rotor Large-Scale Rotor Performance/Wing Download Test and Comparison with Theory, Vertica, 1986, 10(3): 281~297.
[71] Felker F. F., et al. Performance and Loads Data from a Hover Test of a 0.658-scale V-22 Rotor and Wind, NASA-TM-89419, 1987
[72] Dingeldein R C. Wind-tunnel Studies of Performance of Multi-Rotor Configurations. National Advisory Committee for Aeronautics, NACA TN 3236, 1954.
[73] Pruyn R R and Alexander W T. The USAavlabs Tandem Rotor Air Loads Measurement Program. Proceedings of the Aerodynamics Testing Conference, 1966.
[74] Huston R J. Wind Tunnel Measurements of Performance, Blade Motions, and Blade Airlords for Tandem-Rotor Configurations with and Without Overlap. National Aeronautics and Space Administration, NASA TN D-1971, 1963.
[75]徐国华,王适存.具有后掠桨尖的旋翼气动特性计算方法.空气动力学学报.1999, 17(03): 356~361.
[76] Xu, G.H. and Newman, S.J. A Full-Span Free-Wake Model Using Circular-Arc Vortex Elements and Incorporating Rotor Trim Analysis.Journal of Aerospace Engineering, 2006, 220(2):145-163.
[77] Xu G.H., Zhao Q. J., Gao Z., et al, Prediction of Aerodynamics Interactions of Helicopter Rotor on Its Fuselage, Chinese Journal of Aeronautics, 2002, 15(01): 12~17.
[78]童自力,孙茂.纵列式及横列式双旋翼流动的N-S方程模拟及气动特性的研究.航空学报,1999, 20(6):489~492.
[79]王平,王适存等.共轴式双旋翼气动特性分析及实验研究.第13届全国直升机年会论文集.1997.
[80]陈铭,胡继忠,曹义华.共轴双旋翼前飞气动特性固定尾迹分析.2004,30(1):74~78.
[81]李春华,徐国华.悬停和前飞状态倾转旋翼自由尾迹分析,空气动力学学报.2005,23(2):152~156
[82]黄水林,徐国华,招启军.纵列式直升机双旋翼流场特性的自由尾迹分析,空气动力学学报.2008.12,26(4): 473~479.
[83]李攀,张学军,陈仁良,双旋翼系统自由尾迹分析,第20届全国直升机年会论文集,2004
[84]唐正飞,李锋,高正,梅卫胜,用三维激光多谱勒测速仪对共轴双旋翼悬停流场的测定,流体力学实验与测量, 1998,12(1),81~87.
[85]邓彦敏等.共轴式直升上下旋翼之间气动干扰的风洞实验研究,航空学报, 2003,24(1),10~14
[86] Zili T., Mao S., Flow Analysis of Twin-Rotor Configurations by Navier-Strokes Simulation. Journal of the American Helicopter Society, 2000.45(2):97~105.
[87] Daminlig C B, and Edward T M. Computational modeling of the CH-47 helicopter in hover. Proceedings of the 2007 DoD High Performance Computing Modernization Program Users Group Conference, IEEE Computer Society, 2007, 98~103.
[88]吴林波:纵列式直升机双旋翼机身流场特性的CFD分析,硕士学位论文,南京,南京航空航天大学,2009.
[89] Leishman J G, Bagai A, Free-Wake Analysis of Twin-Rotor Systems, Proceedings of the 20th European Rotorcraft Forum, 1994.
[90] Bagai A, Leishman J G, Park J., Aerodynamic Analysis of A Helicopter in Steady Maneuvering Flight using a Free-Vortex Rotor Wake Model. Journal of the American Helicopter Society, 1999.
[91] He, C.J., Development and Application of a Generalized Dynamic Wake Theory for Lifting Rotors, Ph.D. thesis, Georgia Institute of Technology, Georgia, 1989.
[92] Leishman, J. G., Principles of Helicopter Aerodynamics, Cambridge University Press, New York, 2000.
[93] Bhagwat M J, Transient Dynamics of Helicopter Rotor Wakes Using a Time-accurate Free-vortex Method, PhD thesis, University of Maryland, Maryland,2001.
[94]赵景根:直升机旋翼/机身气动干扰的研究,硕士学位论文,南京航空航天大学,南京,2001.
[95]胡健伟、汤怀民,微分方程数值方法,科学出版社,2003.
[96] Carver, M. B., and Hinds, H. W., the Method of Lines and the Advection Equation, Simulation, Vol., 1978, 31(2):59~69.
[97] Schiesser, W. E., the Numerical Method of Lines: Integration of Partial Differential Equations, Academic Press, San Diego, 1991.
[98]关治、陆金甫,数值分析基础,高等教育出版社,2005.
[99] M. N. O. Sadiku and C. N. Obiozor, a Simple Introduction to the Method of Lines,International Journal of Electrical Engineering Education, 2000, 282~296.
[100] Bhagwat M J, Leishman J G, Correlation of Helicopter Tip Vortex Measurements, AIAA Journal, 2000, 38(2):301~308.
[101] Vatistas G H, New Model for Intense Self-Similar Vortices, Journal of Propulsion and Power, 1998, 14(4): 462~469.
[102] Vatistas G H, Kozel V, Mih W C, A Simpler Model for Concentrated Vortices, Experiments in Fluids, 1991, 11:73~76.
[103] Bhagwat M J, Transient Dynamics of Helicopter Rotor Wakes Using a Time-accurate Free-vortex Method, PhD thesis, University of Maryland, 2001.
[104] Bagai A, Contributions to the Mathematical Modeling of Rotor Flow-Fields using a Pseudo-Implicit Free-Wake Analysis, PhD thesis, University of Maryland, Maryland,1995.
[105] Lorber P. F., Stauter R. C., Landgrebe A. J., A Comprehensive Hover Test of the Airloads and Airflow of an Extensively Instrumented Model Helicopter Rotor. Proceedings of the American Helicopter Society 45th Annual Forum, 1989.
[106] Petot, D., Stall Effects and Blade Torsion-An Evaluation of Predictive Tools, Journal of the American Helicopter Society, 1999, 44(4):320~331.
[107] Beddoes T S, Representation of Airfoil Behavior, Vertica, 1983, 7(2):183~197.
[108] Leishman, J.G.., Validation of Approximate Indicial Aerodynamic Functions for Two-Dimensional Subsonic Flow. Journal of Aircraft, 1988, 25(10):510~521.
[109] Leishman, J.G., and Nguyen, K.Q. State-Space Representation of Unsteady Airfoil Behavior. AIAA Journal, 1990, 28(5):20~28.
[110] Thwaites B, Incompressible Aerodynamics, Oxford Univ. Press, Oxford, UK, 1960.
[111] Xu Guohua, Newman S J., Helicopter Rotor Free Wake Calculations Using a New Relaxation Technique,the 26th European Rotorcraft Forum, Netherlands,2000
[112] Leishman, J.G., Bagai A. Fundamental Studies of Rotor Wakes in Low Speed Forward Flight Using Wide-Field Shadowgraphy. Proceedings of AIAA 9th Applied Aerodynamics Meeting, 1991.
[113]王适存主编,直升机空气动力学,航空专业教材编审组,1983.
[114] Lorber P. F. and Egolf T. A., an Unsteady Helicopter Rotor-Fuselage Aerodynamic Interaction Analysis, Journal of the American Helicopter Society, 1990, 35(3):120~128.
[115] Leishman J.G. and Bi N.P., Measurement of a Rotor Flowfield and the Effects on a Fuselage in Forward Flight, Vertica, 1990. 14(3), 401~415.
[116] Leishman J.G., Bi N.P.and D.K. etc., Investigation of Aerodynamic Interactions Between a Rotor and a Fuselage in Forward Flight, Presented at the 45th Annual Forum of the AmericanHelicopter Society, Boston, MA, May 1989, 591~601.
[117] Bagai, A., Leishman, J. G., Rotor Free Wake Modeling Using Relaxation Technique-Including Comparisons with Experimental Data. Journal of the American Helicopter Society, 1995, 40(3):122~129.
[118] R.W.普罗蒂,直升机性能及稳定性和操作性,高正等译,航空工业出版社,1990.
[119]郭才根,郭士龙,直升机总体设计,航空工业出版社,1993.
[120] Tangler, J. L., Wohlfeld, R. M., and Miley, S. J., An Experimental Investigation of Vortex Stability, Tip Shapes, Compressibility, and Noise for Hovering Model Rotors, NASA CR-2305, 1973.
[121] Leishman, J. G., Baker, A., and Coyne, A., Measurements of Rotor Tip Vortices Using Three-Component Laser Doppler Velocimetry, Journal of the American Helicopter Society, , 1996, 41(4) 342~353.
[122] Martin, P. B., Pugliese, G. J. and Leishman, J. G., Stereoscopic PIV Measurements in the Wake of a Hovering Rotor, Proceedings of the American Helicopter Society 56th Annual Forum, 2000.
[123] Bhagwat, M. J., and Leishman, J. G., Stability Analysis of Helicopter Rotor Wakes in Axial Flight, Journal of the American Helicopter Society, 2000, 45(2),165~178