基于尾迹分析的旋翼旋转噪声计算及桨-涡干扰噪声研究
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摘要
旋翼噪声是直升机空气动力学领域具有挑战性的研究课题。基于尾迹分析,本文一方面针对悬停和前飞状态旋翼旋转噪声的计算方法和参数影响进行了研究,另一方面,针对桨-涡干扰(BVI)噪声的探测方法以及BVI噪声在近场与远场传播的方向性和辐射强度进行了深入分析,同时对新型桨尖旋翼的BVI噪声辐射特性及参数影响进行了计算。主要进行了以下几方面工作:
作为前提和背景,本文首先阐述了论文的研究目的,并对直升机旋翼旋转噪声计算、BVI噪声探测及方向性与辐射特性、尾迹分析等研究的国内外现状进行了概述,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。为准确计算旋翼气动载荷和噪声提供翼型气动模型,本文第二章基于Leishman-Beddoes模型,建立了一个附着流、分离流和失速流状态下的翼型非定常气动力数值计算方法,并进行了方法验证。
为了用于旋转噪声的计算和桨-涡干扰的探测,本文建立了一个适于悬停和前飞状态的旋翼自由尾迹模型。应用该模型,计算了不同前进比下的旋翼自由尾迹形状、桨盘诱导入流分布以及桨叶载荷分布,验证了模型的有效性。基于Farassat 1A声学时域公式以及该自由尾迹模型,本文发展了一套适合于悬停和前飞状态下旋翼旋转噪声计算的方法。应用所建立的方法,分别进行了旋翼厚度和载荷噪声的计算,并对旋翼转速、桨叶片数、旋翼直径等不同设计参数对旋转噪声的影响进行了研究,得到了一些有实际意义的结果。
然后,基于Beddoes修正尾迹模型,建立了一个新的用于旋翼前行侧和后行侧BVI噪声辐射特性和方向性分析的模型,研究了BVI噪声在前行侧和后行侧的分布特点,分析了桨叶片数、前进比、桨尖马赫数等不同参数对BVI噪声辐射特性和方向性的影响,总结出了一些BVI噪声前行侧和后行侧辐射的规律。在此基础上,本文又进一步推导和建立了一个新的用于后掠、前掠和锯齿新型桨尖旋翼BVI噪声辐射特性的分析方法,使用该方法研究了这些新型桨尖旋翼发生BVI时的特点,以及后掠、前掠和锯齿桨尖对旋翼桨-涡干扰噪声方向性的影响,得出了对降低桨-涡干扰噪声设计具有指导意义的结论。
最后,基于自由尾迹分析模型,还建立了一个适合于旋翼桨-涡干扰垂直距离的平面探测方法,使用该探测方法,计算了不同状态下旋翼桨-涡干扰时的桨涡垂直距离,着重分析了桨叶片数、前进比、桨盘迎角等不同参数对桨-涡干扰垂直距离和桨-涡干扰角的影响。
Rotor noise is a challenging subject in the field of helicopter aerodynamics. Based on wake analysis, on one hand, the computational method for rotor rotational noise in hover and forward flight and the effect of parameters are investigated in this thesis. On the other hand, the detective method on blade-vortex interaction and directionality of its noise in the near/far field and radiation intensity are deeply analyzed. Also, the radiation characteristics about BVI noise of modern rotors with new blade tips and parameter influences are investigated. The major contributions of the author’s research work are as follows:
As the background of present work, the objectives of the research are firstly described. The research and development in the field of the helicopter rotor rotational noise, blade-vortex interaction sources detection, directionality and radiation characteristic of BVI noise, as well as wake analysis are briefly introduced. The difficulties in the current research on the BVI noise are pointed out. In addition, the methods used in the present research are briefly introduced. In order to provide an accurate airfoil aerodynamic model for computation of the rotor aerodynamic loading and noise, Chapter 2 establishes a method of computing airfoil unsteady aerodynamic forces at the attached flow, separated flow and stalled flow, based upon the Leishman-Beddoes model. The comparisons with the available experimental data are also made to show the capability of the method.
Aiming at rotational noise computation and BVI detection, a free-wake model for hover and forward flight rotor is presented. By using this model, the free-wake geometry, induced inflow and loading distribution of the rotor at different advance ratios are calculated for validation purposes. By employing Farassat Acoustic Formula 1A in the time domain and combining the free-wake model, a numerical method of rotational noise computation for hover and forward flight has been developed. By the method developed, both rotor thickness and loading noise are computed. The influence of different design parameters on the rotational noise, such as rotor speed, blade number and rotor diameter, are also investigated. On the basis of the investigation, some meaningful results are obtained.
Then, a new model for studying BVI noise directionality and radiation characteristics at the advancing side and retreating side of a rotor is developed with the help of the Beddoes modified wake model. The distribution features of BVI noise at the rotor advancing side and retreating side are studied, and the effect of different parameters such as blade number, advance ratio and tip Mach number, are also analyzed. Some conclusions have been drawn from analyzing the BVI noise radiation characteristics. Furthermore, a novel method of analyzing BVI noise radiation characteristics for the rotor with new blade tips such as backward-swept tip, forward-swept tip and sawtooth tip, is derived and established in this thesis. The features of the rotor BVI noise radiation with these modern blade-tips are investigated by using the method, and the influences of these modern tips on rotor BVI noise directionality and radiation characteristics are also discussed. Based on the research, some results which are helpful for the rotor design of reducing BVI noise are obtained.
Finally, applying the free wake model, a plane detection method for rotor BVI miss-distance detection is developed. From this method, the miss-distance of BVI at the different conditions is computed, and the influences of the blade number, advance ratio and attack angle of tip-path-plane on the miss-distance and blade-vortex angle are emphatically analyzed.
作为前提和背景,本文首先阐述了论文的研究目的,并对直升机旋翼旋转噪声计算、BVI噪声探测及方向性与辐射特性、尾迹分析等研究的国内外现状进行了概述,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。为准确计算旋翼气动载荷和噪声提供翼型气动模型,本文第二章基于Leishman-Beddoes模型,建立了一个附着流、分离流和失速流状态下的翼型非定常气动力数值计算方法,并进行了方法验证。
为了用于旋转噪声的计算和桨-涡干扰的探测,本文建立了一个适于悬停和前飞状态的旋翼自由尾迹模型。应用该模型,计算了不同前进比下的旋翼自由尾迹形状、桨盘诱导入流分布以及桨叶载荷分布,验证了模型的有效性。基于Farassat 1A声学时域公式以及该自由尾迹模型,本文发展了一套适合于悬停和前飞状态下旋翼旋转噪声计算的方法。应用所建立的方法,分别进行了旋翼厚度和载荷噪声的计算,并对旋翼转速、桨叶片数、旋翼直径等不同设计参数对旋转噪声的影响进行了研究,得到了一些有实际意义的结果。
然后,基于Beddoes修正尾迹模型,建立了一个新的用于旋翼前行侧和后行侧BVI噪声辐射特性和方向性分析的模型,研究了BVI噪声在前行侧和后行侧的分布特点,分析了桨叶片数、前进比、桨尖马赫数等不同参数对BVI噪声辐射特性和方向性的影响,总结出了一些BVI噪声前行侧和后行侧辐射的规律。在此基础上,本文又进一步推导和建立了一个新的用于后掠、前掠和锯齿新型桨尖旋翼BVI噪声辐射特性的分析方法,使用该方法研究了这些新型桨尖旋翼发生BVI时的特点,以及后掠、前掠和锯齿桨尖对旋翼桨-涡干扰噪声方向性的影响,得出了对降低桨-涡干扰噪声设计具有指导意义的结论。
最后,基于自由尾迹分析模型,还建立了一个适合于旋翼桨-涡干扰垂直距离的平面探测方法,使用该探测方法,计算了不同状态下旋翼桨-涡干扰时的桨涡垂直距离,着重分析了桨叶片数、前进比、桨盘迎角等不同参数对桨-涡干扰垂直距离和桨-涡干扰角的影响。
Rotor noise is a challenging subject in the field of helicopter aerodynamics. Based on wake analysis, on one hand, the computational method for rotor rotational noise in hover and forward flight and the effect of parameters are investigated in this thesis. On the other hand, the detective method on blade-vortex interaction and directionality of its noise in the near/far field and radiation intensity are deeply analyzed. Also, the radiation characteristics about BVI noise of modern rotors with new blade tips and parameter influences are investigated. The major contributions of the author’s research work are as follows:
As the background of present work, the objectives of the research are firstly described. The research and development in the field of the helicopter rotor rotational noise, blade-vortex interaction sources detection, directionality and radiation characteristic of BVI noise, as well as wake analysis are briefly introduced. The difficulties in the current research on the BVI noise are pointed out. In addition, the methods used in the present research are briefly introduced. In order to provide an accurate airfoil aerodynamic model for computation of the rotor aerodynamic loading and noise, Chapter 2 establishes a method of computing airfoil unsteady aerodynamic forces at the attached flow, separated flow and stalled flow, based upon the Leishman-Beddoes model. The comparisons with the available experimental data are also made to show the capability of the method.
Aiming at rotational noise computation and BVI detection, a free-wake model for hover and forward flight rotor is presented. By using this model, the free-wake geometry, induced inflow and loading distribution of the rotor at different advance ratios are calculated for validation purposes. By employing Farassat Acoustic Formula 1A in the time domain and combining the free-wake model, a numerical method of rotational noise computation for hover and forward flight has been developed. By the method developed, both rotor thickness and loading noise are computed. The influence of different design parameters on the rotational noise, such as rotor speed, blade number and rotor diameter, are also investigated. On the basis of the investigation, some meaningful results are obtained.
Then, a new model for studying BVI noise directionality and radiation characteristics at the advancing side and retreating side of a rotor is developed with the help of the Beddoes modified wake model. The distribution features of BVI noise at the rotor advancing side and retreating side are studied, and the effect of different parameters such as blade number, advance ratio and tip Mach number, are also analyzed. Some conclusions have been drawn from analyzing the BVI noise radiation characteristics. Furthermore, a novel method of analyzing BVI noise radiation characteristics for the rotor with new blade tips such as backward-swept tip, forward-swept tip and sawtooth tip, is derived and established in this thesis. The features of the rotor BVI noise radiation with these modern blade-tips are investigated by using the method, and the influences of these modern tips on rotor BVI noise directionality and radiation characteristics are also discussed. Based on the research, some results which are helpful for the rotor design of reducing BVI noise are obtained.
Finally, applying the free wake model, a plane detection method for rotor BVI miss-distance detection is developed. From this method, the miss-distance of BVI at the different conditions is computed, and the influences of the blade number, advance ratio and attack angle of tip-path-plane on the miss-distance and blade-vortex angle are emphatically analyzed.
引文
[1] Johnson W, Helicopter Theory, Princeton University Press, 1980.
[2] George A R, Helicopter Noise: State-of-the-Art, Journal of Aircraft, 1978, 15(11):707~715.
[3] Sternfeld H Jr, Advanced Rotorcraft Noise, AIAA, 80-0857, 1980.
[4] Brentner K S, Farassat F, Helicopter Noise Prediction: the Current Status and Future Direction, Journal of Sound and Vibration, 1994, 170(1):79~96.
[5] Farassat F, Succi G P, The Prediction of Helicopter Rotor Discrete Frequency Noise, Proceedings of the American Helicopter Society 38th Annual Forum, 1982.
[6] Schultz K J, Splettstoesser W R, Prediction of Helicopter Rotor Impulsive Noise Using Measured Blade Pressures, Proceedings of the American Helicopter Society 43rd Annual Forum, 1987.
[7] Sim B W-C, George A R, Development of a Rotor Aerodynamic Load Prediction Scheme for Blade-Vortex Interaction Noise Study, Proceedings of the American Helicopter Society 51st Annual Forum, 1995.
[8] Schmitz F H, Boxwell D A, Splettstoesser W R, et al., Model-Rotor High-Speed Impulsive Noise: Full-Scale Comparisons and Parametric Variations, Vertica, 1984, 8(4):395~422.
[9] Brentner K S, An Efficient and Robust Method for Predicting Helicopter Rotor High-Speed Impulsive Noise, Journal of Sound and Vibration, 1997, 203(1):87~100.
[10] Brentner K S, Farassat F, An Analytical Comparison of the Acoustic Analogy and Kirchhoff Formulation for Moving Surfaces, Proceedings of the American Helicopter Society 53th Annual Forum, 1997.
[11] Ffowcs W J E, Hawkings D L, Sound Generation by Turbulence and Surfaces in Arbitrary Motion, Mathematical and Physical Sciences, 1969, 264(1151):321~342.
[12] Farassat F, Derivation of Formulations 1 and 1A of Farassat, NASA TM-214853, 2007.
[13] Farassat F, Linear Acoustic Formulas for Calculation of Rotating Blade Noise, AIAA Journal, 1981, 19(9):1121~1130.
[14] Brentner K S, Prediction of Helicopter Rotor Discrete Frequency Noise for Three Scale Models, Journal of Aircraft, 1988, 25(5):420~427.
[15] Ffowcs W J E, Hawkings D L, Theory Relating to the Noise of Rotating Machinery, Journal of Sound and Vibration, 1969,10(1):10~21.
[16] Lowson M V, Ollerhead J B, A Theoretical Studies of Helicopter Rotor Noise, Journal of Sound and Vibration, 1969, 9(2):197~222.
[17] Schmitz F H, Rotor Noise, Aeroacoustics of Flight Vehicles: Theory and Practice, 1991, 1:65~149.
[18] Farassat F, Brentner K S, The Influence of Quadrupole Sources in the Boundary Layer and Wake of a Blade on Helicopter Rotor Noise, Proceedings of International Specialists Meeting, 1991.
[19] Prichard D S, Boyd D D, Burley C L, NASA/Langley's CFD-Based BVI Rotor Noise Prediction Systems: (ROTORNET/FPRBVI) An Introduction and User's Guide, NASA TM-109147, 1994.
[20] Farassat F, Succi G P, The Prediction of Helicopter Rotor Discrete Frequency Noise, Vertica, 1983, 7(4):309~320.
[21] Brentner K S, Prediction of Helicopter Rotor Discrete Frequency Noise—A Computer Program Incorporating Realistic Motions and Advanced Acoustic Formulation, NASA TM-87721, 1986.
[22] Brentner K S, Brès G A, Perez G. et al., Maneuvering Rotorcraft Noise Prediction: A New Code for a New Problem, Proceedings of the AHS Aerodynamics, Acoustics, and Test Evaluation Specialist Meeting, 2002.
[23] Lewy S, Caplot M, Review of Some Theoretical and Experimental Studies on Helicopter Rotor Noise, Vertica, 1984, 8(4):309~321.
[24] Visintainer J A, Marcolini M A, Burley C L, et al., Acoustic Predictions Using Measured Pressures from a Model Rotor in the DNW, Journal of AHS, 1993, 38(3):35~44.
[25] Brentner K S, Lyrintzis A S, Koutsavdis E K, Comparison of Computational Aeroacoustic Prediction Methods for Transonic Rotor Noise Prediction, Journal of Aircraft, 1997, 34(4):531~538.
[26]段广战,陈平剑,基于CFD的直升机旋翼噪声计算,空气动力学学报, 2009, 27(3):314~319.
[27] Widnall S E, Helicopter Noise Due to Blade-Vortex Interactions, Journal of the Acoustical Society of America, 1971, 50(1): 354~365.
[28] Munsky B, Gandhi F, Tauszig L, Analysis of Helicopter Blade-Vortex Interaction Noise with Flight Path or Attitude Modification, Journal of American Helicopter Society, 2005, 50(2):123~137.
[29] Woo S, Oh K-W, Two-Dimensional BVI Revisited Using Unstructured Dynamic Meshes, Proceedings of the American Helicopter Society 58th Annual Forum, 2002.
[30] M. V. Lowson, Focusing of Helicopter BVI Noise, Journal of Sound and Vibration, 1996, 190(3):477~494.
[31] Schmitz F H, Sim B W-C, Radiation and Directionality Characteristics of Helicopter Blade-Vortex Interaction Noise, Journal of the American Helicopter Society, 2003, 48(4): 253~269.
[32] Gopalan G, Schmitz F H, Quasi-Static Flight Path Control of Helicopter Blade Vortex Interaction Noise in a Steady Wind, Journal of the American Helicopter Society, 2007, 52(1):15~23.
[33] Ringler T D, George A R, Steele J B, A Study of Blade-Vortex Interaction Sound Generation and Directionality, Proceedings of the AHS and Royal Aeronautical Society, Technical Specialists' Meeting on Rotorcraft Acoustics/Fluid Dynamics, 1991.
[34] Schmitz F H, Reduction of Blade Vortex Interaction (BVI) Noise Through X-force Control, Journal of the American Helicopter Society, 1998, 43(14): 14~24.
[35] Yu Y H, Rotor Blade Vortex Interaction Noise, Progress in Aerospace Sciences, 2000, 36:97~115.
[36] Chehab M, W?lk J, A Windtunnel Study of X-Force Generators to Reduce Helicopter Blade-Vortex Interaction (BVI) Noise, Proceedings of the AIAA Student Design Conference, 2000.
[37] Schmitz F H, Gopalan G, Sim B-C, Flight Trajectory Management to Reduce Helicopter Blade-Vortex Interaction(BVI) Noise with Head/Tailwind Effects, Proceedings of the 26th European Rotorcraft Forum, 2000.
[38] Kuo B C, Sim B W-C, Schmitz F H, Blade-Vortex Interaction Wave Radiation Patterns of Helicopter Blades With Different Leading-Edge Geometry, Proceedings of the American Helicopter Society 58th Annual Forum, 2002.
[39]王华明,张强,胡章伟等, AS350B2直升机飞行噪声的试验研究,声学学报, 2003, 38(2):177~181.
[40]徐国华,高正,悬停状态下模型旋翼噪声试验的初步研究,空气动力学学报, 1996, 14(1):68~72.
[41]徐国华,高正,直升旋翼旋转噪声的估算,南京航空航天大学学报, 1991, 23(2):20~26.
[42]李启,张强,刘建付,直升机尾桨定常载荷噪声的工程计算方法,南京航空航天大学学报, 2006, 38 (2):136~142.
[43]王华明,陈本现,悬停状态下旋翼旋转噪声的分析,南京航空航天大学学报, 2003, 35(3):273~276.
[44]宋文萍,韩忠华,杨爱明等,旋翼跨声速流动气动噪声的一种高效算法,西北工业大学学报, 2001, 19(4):515~519.
[45]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.
[46]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.
[47]招启军,徐国华,王适存,基于CFD/Kirchhoff方法的直升机旋翼高速脉冲噪声模拟分析,计算物理, 2006, 23(2):137~143.
[48]曹义华,康鹏斌,于子文,旋翼翼型-桨尖涡干扰的数值模拟,航空动力学报, 2003, 18(5):604~607.
[49] Castles W, Durham H L, Distribution of Normal Component of Induced Velocity in Lateral Plane of a Lifting Rotor, NACA TN-3841, 1956.
[50] 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.
[51] Kocurek J D, Tangler J L, A Prescribed Wake Lifting Surface Hover Performance Analysis, Journal of the American Helicopter Society, 1977, 22(1):24~35.
[52]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.
[53] Martin P B, Bhagwat M J, Leishman J G, Visualization of a Helicopter Rotor Wake in Hover, AIAA 9923225, 1999.
[54]王适存主编,直升机空气动力学,航空专业教材编审组, 1983.
[55] Landgrebe A J, An Analytical and Experimental Investigation of Helicopter Rotor Hover Performance and Wake Geometry Characteristics, USA AMRDL TR-71224, 1971.
[56] Shenoy K R, Gray R B, Iterative Lifting Surface Method for Thick Bladed Hovering Helicopter Rotors, Journal of Aircraft, 1981, 18(6): 417~424.
[57]王适存,升力螺旋桨在桨盘上的诱导速度分布,力学学报, 1964, 7(3):211~221.
[58]王适存,徐国华,直升机旋翼空气动力学的发展,南京航空航天大学学报, 2001, 33(3):203~211.
[59] Beddoes T S, A Wake Model for High Resolution Airloads, Proceedings of the International Conference on Rotorcraft Basic Research, 1985.
[60] Landgrebe A J, Prediction of Helicopter Induced Flow Velocities Using the Rotorcraft Wake Ananlysis, Proceedings of the 32nd Annual Forum of the American Helicopter Society, 1976.
[61] Quackenbush T R, Lam C M G, Wachspress D A, et al., Analysis of High Resolution Unsteady Airloads for Helicopter Rotor Blades, Proceedings of the American Helicopter Society 50thAnnual Forum, 1994.
[62] 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.
[63] Sadler S G, Development and Application of a Method for Predicting Rotor Free Wake Positions and Resulting Rotor Blade Air Loads, 1971.
[64] Scully M. P.: A Method of Computing Helicopter Vortex Wake Distortion, Massachusetts Institute of Technology, ASRL TR-138-1, 1967.
[65] 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.
[66] Miller R H, A Simplified Approach to the Free Wake Analysis of a Hovering Rotor, Proceedings of the 7th European Rotorcraft Forum , 1981.
[67] Egolf T A, Sparks S P, A Full Potential Rotor Analysis with Wake Influence Using an Inner-Outer Domain Technique, Proceedings of the 42nd Annual AHS Forum, 1986.
[68] Bliss D B, Dadone L, Wachspress D A, Rotor Wake Modeling for High Speed Applications, Proceedings of the American Helicopter Society 43rd Annual Forum, 1987.
[69] Johnson W, A Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dynamics, NASA TM-81182, 1982.
[70] He C, Lee C S, Chen W, Rotorcraft Simulation Model Enhancement to Support Design, Testing and Operational Analysis, Journal of the American Helicopter Society, 2000, 45(4):284~292.
[71]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.
[72] Crouse, Jr G L, Leishman J G, A New Method for Improved Rotor Free Wake Convergence, Proceedings of the 31st AIAA Aerospace Sciences Meeting and Exhibit, 1993.
[73] Bagai A, Leishman J G, Rotor Free-Wake Modeling Using a Relaxation Technique -Including Comparisons with Experimental Data, Journal of the American Helicopter Society, 1995, 40(3):29~41.
[74] Bhagwat M J, Leishman J G, Rotor Aerodynamics During Maneuvering Flight Using a Time-Accurate Free-vortex Wake , Journal of the American Helicopter Society, 2003, 48(3):143~158.
[75]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):54~59.
[76]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.
[77]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.
[78] Xu G H, Zhao Q J, Gao Z, et al., Prediction of Aerodynamic Interactions of Helicopter Rotor on Its Fuselage, Chinese Journal of Aeronautics, 2002, 15(1):12~17.
[79] He C, Zhao J, Modeling Rotor Wake Dynamics with Viscous Vortex Particle Method, AIAA Journal, 2009, 47(4):902~913.
[80]岳海龙,夏品奇,倾转旋翼机在转换飞行时的旋翼尾迹弯曲非定常动态入流模型,中国科学(E辑:技术科学), 2009, 39(12):1992~2000.
[81] Li P, Chen R, Aerodynamics Analysis of a Rotor Undergoing Maneuvers Using an Efficient Time Marching Free Vortex Method, Proceedings of the 3rd International Basic Research Conference on Rotorcraft Technology, 2009.
[82] Tauszig L, Numerical Detection and Characterization of Blade Vortex Interactions Using a Free Wake Analysis, Master Thesis, Pennsylvania State University, 1998.
[83] Johnson W, Rotorcraft Aerodynamics Models for a Comprehensive Analysis, Proceedings of the 54th AHS Annual Forum, 1998.
[84] Leishman J G, Challenges in Modeling the Unsteady Aerodynamics of Wind Turbines, Proceedings of the 40th AIAA Aerospace Sciences Meeting, 2002.
[85] Martin P B, McAlister K W, Chandrasekhara M S, Dynamic Stall Measurements and Computations for a VR-12 Airfoil with a Variable Droop Leading Edge, Proceedings of the American Helicopter Society 59th Annual Forum, 2003.
[86] Nguyen K, Johnson W, Evaluation of Dynamic Stall Models with UH-60A Airloads Flight Test Data, Proceedings of the American Helicopter Society 54th Annual Forum, 1998.
[87] Hyeonsoo Y, Calculation of Rotor Performance and Loads under Stalled Conditions, Proceedings of the 59th AHS Annual Forum, 2003.
[88] Leishman J G, Beddoes T S, A Semi-Empirical Model for Dynamic Stall, Proceedings of the 42nd AHS Annual Forum, 1986.
[89] Leishman J G, Beddoes T S. A Generalized Model for Unsteady Airfoil Behavior and Dynamic Stall Using the Indicial Method, Proceedings of the 42nd AHS Annual Forum, 1986.
[90] Leishman J G, Validation of Approximate Indicial Aerodynamic Functions for Two-dimensional Subsonic Flow, Journal of Aircraft, 1988, 25(10): 914~922.
[91] Beddoes T S, Onset of Leading Edge Separation Effects under Dynamic Conditions and LowMach Number, Proceedings of the 34th AHS Annual Forum, 1978.
[92] Hilaire A, Carta F O, Fink M R, et al., The Influence of Sweep on the Aerodynamic Loading of a NACA0012 Airfoil, NASA CR-3092 1979.
[93] Leishman J G, Lee D, Baeder J D, A Nonlinear Indicial Method for the Calculation of Unsteady Airloads, Proceedings of the 59th AHS Annual Forum, 2003.
[94] Carlson H W, Mack R J, Studies of Leading Edge Thrust Phenomena, Journal of Aircraft, 17(12): 890~897, 1980.
[95] Leishman J G, Modeling Sweep Effects on Dynamic stall, Journal of the AHS, 1989, 34(3):18~29.
[96] Leishman J G, Principles of Helicopter Aerodynamics, Cambridge University Press, 2000.
[97] Bagai A, Contributions to the Mathematical Modeling of Rotor Flow-Fields Using a Pseudo-Implicit Free-Wake Analysis, PhD thesis, University of Maryland, 1995.
[98]黄水林,纵列式直升机双旋翼气动干扰特性的理论与试验研究,博士学位论文,南京航空航天大学, 2009.
[99] Bhagwat M J, Transient Dynamics of Helicopter Rotor Wakes Using a Time-Accurate Free-Vortex Method, PhD thesis, University of Maryland, 2001.
[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] Bagai A, Leishman J G, Rotor Free-Wake Modeling Using a Pseudo-Implicit Algorithm. Journal of Aircraft, 1995, 32(6):1276~1285.
[103] 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.
[104]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气动干扰计算,空气动力学学报, 2007, 25(3):390~395.
[105]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.
[106] Caradonna F X, Tung C, Experimental and Analytical Studies of a Model Helicopter Rotor in Hover, NASA TM-81232, 1981.
[107] Leishman J G, Bagai A, Fundamental Studies of Rotor Wakes in Low Speed Forward Flight Using Wide-field Shadowgraphy, AIAA Paper 91-3232, 1991.
[108] Scheiman J, A Tabulation of Helicopter Rotor-Blade Differential Pressures, Stress and Motions Measured in Flight, NASA TM-X952, 1964.
[109]徐国华,直升机旋翼噪声分析及估算方法,硕士论文,南京航空学院, 1990.
[110] Dahan C, Gratieux E, Helicopter Rotor Thickness Noise, AIAA-80-1012R, 1980.
[111] Brentner K S, Numerical Algorithms for Acoustic Integrals with Examples for Rotor Noise Prediction, AIAA Journal, 1997, 35(4):625~630.
[112] Brentner K S, Farassat F, Modeling Aerodynamically Generated Sound of Helicopter Rotors, Progress in Aerospace Science, 2003, 39(2-3):83~120.
[113] ?zy?rük Y, Alpmana E, Ahujab V, et al., Frequency-Domain Prediction of Turbofan Noise Radiation, Journal of Sound and Vibration, 2004, 270(4-5):933~950.
[114] Strawn R C, Biswas R, Lyrintzis A S, Helicopter Noise Predictions Using Kirchhoff Methods, Journal of Computational Acoustics 1996, 4(3): 321~339.
[115] Farassat F, Acoustic Radiation from Rotating Blades—the Kirchhoff Method in Aeroacoustics, Journal of Sound and Vibration, 2001, 239(4):785~800.
[116] Singh R K, Transonic Effects on Aerodynamics and Acoustics of Blade-Vortex Interaction, PhD thesis, University of Maryland, 1999.
[117] Kuntz M, Rotor Noise Predictions in Hover and Forward Flight Using Different Aeroacoustic Methods, AIAA 96-1695, 1996.
[118] Sim B W-C, Schmitz F H, Blade-Vortex Interaction (BVI) Noise: Retreating Side Characteristics, Sensitivity to Chordwise Loading and Unsteady Aerodynamics,Proceedings of the American Helicopter Society Aeromechanics Specialists’Meeting, 2000.
[119] Daniel G. O, et al, Rotorcraft Aerodynamic and Aeroacoustic Modelling Using Vortex Particle Methods, Proceedings of the 23rd International Council of the Aeronautical Sciences, 2002.
[120] Caradonna F, Kitapliogiu C, Method for the Prediction of Blade-Vortex Interaction Noise, Proceedings of the American Helicopter Society Technical Specialists’Meeting for Rotorcraft Acoustics and Aerodynamics, 1997.
[121] Purcell T W, CFD and Transonic Helicopter Sound, Proceedings of the 14th European Rotorcraft Forum, 1988.
[122] Landgrebe A F, Bellinger E D, An Investigation of the Quantitative Applicability of Model Helicopter Rotor Wake Patterns Obtained From a Water Tunnel, USAAMRDL TR 71-69, 1971.
[123] Sim B W-C, Near/Far-Field Radiation Characteristics of Advancing Side HelicopterBlade-Vortex Interaction (BVI) Noise, Proceedings of the American Helicopter Society 56th Annual National Forum, 2000.
[124] Nakamura Y, Prediction of Blade-Vortex Interaction Noise from Measured Blade Pressure, Proceedings of the 7th European Rotorcraft and Powered Lift Aircraft Forum, 1981.
[125]超级战斗机突破音障瞬间的精美照片, http://www.chinanews.com.cn/tp/news/2009/05-30/1711959.shtml,2009.
[126] Leishman J G, Sound Directivity Generated by Helicopter Rotors Using Wave Tracing Concepts, Journal of Sound and Vibration, 1999,221(3): 415~441.
[127] Sim B W, Schmitz F H, Acoustic Phasing and Amplification Effects of Single Rotor Helicopter Blade-Vortex Interactions, Proceedings of the American Helicopter Society 55th Annual Forum, 1999.
[128] Sim B W-C, George A R, Yen S J, Blade Vortex Interaction Directivity Studies Using Trace Mach Number, Proceedings of 2nd AHS Aeromechanics Specialists’Conference, 1995.
[129] Sim W-C, Blade-Vortex Interaction Noise Generation and Directionality, PhD thesis, Conell University, 1996.
[130] Hu H, Jordan Jr L A, Beader J D, CFD Investigation of Double-Swept Blade in BVI Noise Reduction, Proceedings of the 9th AIAA/CEAS Aeroacoustics Conference and Exhibit, 2003.
[131] Hoad D R, Evaluation of Helicopter Noise due to Blade-Vortex Interaction for Five Tip Configurations, NASA TM-1608, 1979.
[132]招启军,新型桨尖旋翼流场及噪声的数值模拟研究,博士学位论文,南京航空航天大学, 2005.
[133] Srinivasan G R, Raghavan V, Duque E P N, et al., Flowfield Analysis of Mordern Helicopter Rotors in Hover by Navier-Stokes Method, Proceedings of the 47th Annual Forum of AHS, 1991.
[134] Lim J W, Strawn R C, Computational Modeling of HART II Blade-Vortex Interaction Loading and Wake System, Journal of Aircraft, 2008, 45(3):923~933.
[135] Tamura A, Tsutahara M, Kataoka T, et al., Numerical Simulation of Two-Dimensional Blade-Vortex Interactions Using Finite Difference Lattice Boltzmann Method, AIAA Journal, 2008, 46(9):2235~2245.
[136] Malovrh B, Gandhi F, Sensitivity of Helicopter Blade-Vortex-Interaction Noise and Vibration to Interaction Parameters, Journal of Aircraft, 2005, 42(3): 685~697.
[137] Yu Y H, Tung C, Gallman J, Aerodynamics and Acoustics of Rotor Blade-VortexInteractions,Journal of Aircraft, 1995, 32(5): 970~977.
[138] Tung C, Kube R, Brooks T F, et al, Prediction and Measurement of Blade–Vortex Interaction, Journal of Aircraft, 1998, 35(2): 260~266.
[139] Lee Y-C, An Experimental and Theoretical Study of Helicopter Rotor Noise,PhD thesis, Massachusetts Institute of Technology, 1975.
[140] George A R, Lyrintzis A S, Acoustics of Transonic Blade-Vortex Interactions, AIAA Journal, 1988, 26(7):769~776.
[141] Epstein R J, Rule J A, Bliss D B, Novel Method for Calculating Two-Dimensional Blade Vortex Interaction, AIAA Journal, 1997, 35(5):909~912.
[142] DuVall T, Sim B W, Schmitz F H, Cabin versus Far-Field Blade-Vortex Interaction Noise Level Trends, Proceedings of the AHS Aerodynamics, Acoustics, and Test Evaluation Technical Specialists Meeting, 2002.
[143] Gervais M, Schmitz F H, Tiltrotor BVI Noise Reduction Through Flight Trajectory Management & Configuration Control, Journal of the AHS, 2004, 49(4):436~446.
[144] Heyson H H, Induced Flow Near a Helicopter Rotor: A Review of Present Knowledge, Journal of Aircraft Engineering and Aerospace Technology, 1993, 31(2):40~44.
[145] AbellóJ C, George A, Wake Displacement Modifications to Reduce Rotorcraft Blade–Vortex Interaction Noise, Journal of Aircraft, 2004, 41(2): 290~303.
[146] Burley C L, Brooks T F, Charles B D, et al, Tiltrotor Aeroacoustic Code (TRAC) Prediction Assessment and Initial Comparisons With TRAM Test Data, Proceedings of the 25th European Rotorcraft Forum, 1999.
[2] George A R, Helicopter Noise: State-of-the-Art, Journal of Aircraft, 1978, 15(11):707~715.
[3] Sternfeld H Jr, Advanced Rotorcraft Noise, AIAA, 80-0857, 1980.
[4] Brentner K S, Farassat F, Helicopter Noise Prediction: the Current Status and Future Direction, Journal of Sound and Vibration, 1994, 170(1):79~96.
[5] Farassat F, Succi G P, The Prediction of Helicopter Rotor Discrete Frequency Noise, Proceedings of the American Helicopter Society 38th Annual Forum, 1982.
[6] Schultz K J, Splettstoesser W R, Prediction of Helicopter Rotor Impulsive Noise Using Measured Blade Pressures, Proceedings of the American Helicopter Society 43rd Annual Forum, 1987.
[7] Sim B W-C, George A R, Development of a Rotor Aerodynamic Load Prediction Scheme for Blade-Vortex Interaction Noise Study, Proceedings of the American Helicopter Society 51st Annual Forum, 1995.
[8] Schmitz F H, Boxwell D A, Splettstoesser W R, et al., Model-Rotor High-Speed Impulsive Noise: Full-Scale Comparisons and Parametric Variations, Vertica, 1984, 8(4):395~422.
[9] Brentner K S, An Efficient and Robust Method for Predicting Helicopter Rotor High-Speed Impulsive Noise, Journal of Sound and Vibration, 1997, 203(1):87~100.
[10] Brentner K S, Farassat F, An Analytical Comparison of the Acoustic Analogy and Kirchhoff Formulation for Moving Surfaces, Proceedings of the American Helicopter Society 53th Annual Forum, 1997.
[11] Ffowcs W J E, Hawkings D L, Sound Generation by Turbulence and Surfaces in Arbitrary Motion, Mathematical and Physical Sciences, 1969, 264(1151):321~342.
[12] Farassat F, Derivation of Formulations 1 and 1A of Farassat, NASA TM-214853, 2007.
[13] Farassat F, Linear Acoustic Formulas for Calculation of Rotating Blade Noise, AIAA Journal, 1981, 19(9):1121~1130.
[14] Brentner K S, Prediction of Helicopter Rotor Discrete Frequency Noise for Three Scale Models, Journal of Aircraft, 1988, 25(5):420~427.
[15] Ffowcs W J E, Hawkings D L, Theory Relating to the Noise of Rotating Machinery, Journal of Sound and Vibration, 1969,10(1):10~21.
[16] Lowson M V, Ollerhead J B, A Theoretical Studies of Helicopter Rotor Noise, Journal of Sound and Vibration, 1969, 9(2):197~222.
[17] Schmitz F H, Rotor Noise, Aeroacoustics of Flight Vehicles: Theory and Practice, 1991, 1:65~149.
[18] Farassat F, Brentner K S, The Influence of Quadrupole Sources in the Boundary Layer and Wake of a Blade on Helicopter Rotor Noise, Proceedings of International Specialists Meeting, 1991.
[19] Prichard D S, Boyd D D, Burley C L, NASA/Langley's CFD-Based BVI Rotor Noise Prediction Systems: (ROTORNET/FPRBVI) An Introduction and User's Guide, NASA TM-109147, 1994.
[20] Farassat F, Succi G P, The Prediction of Helicopter Rotor Discrete Frequency Noise, Vertica, 1983, 7(4):309~320.
[21] Brentner K S, Prediction of Helicopter Rotor Discrete Frequency Noise—A Computer Program Incorporating Realistic Motions and Advanced Acoustic Formulation, NASA TM-87721, 1986.
[22] Brentner K S, Brès G A, Perez G. et al., Maneuvering Rotorcraft Noise Prediction: A New Code for a New Problem, Proceedings of the AHS Aerodynamics, Acoustics, and Test Evaluation Specialist Meeting, 2002.
[23] Lewy S, Caplot M, Review of Some Theoretical and Experimental Studies on Helicopter Rotor Noise, Vertica, 1984, 8(4):309~321.
[24] Visintainer J A, Marcolini M A, Burley C L, et al., Acoustic Predictions Using Measured Pressures from a Model Rotor in the DNW, Journal of AHS, 1993, 38(3):35~44.
[25] Brentner K S, Lyrintzis A S, Koutsavdis E K, Comparison of Computational Aeroacoustic Prediction Methods for Transonic Rotor Noise Prediction, Journal of Aircraft, 1997, 34(4):531~538.
[26]段广战,陈平剑,基于CFD的直升机旋翼噪声计算,空气动力学学报, 2009, 27(3):314~319.
[27] Widnall S E, Helicopter Noise Due to Blade-Vortex Interactions, Journal of the Acoustical Society of America, 1971, 50(1): 354~365.
[28] Munsky B, Gandhi F, Tauszig L, Analysis of Helicopter Blade-Vortex Interaction Noise with Flight Path or Attitude Modification, Journal of American Helicopter Society, 2005, 50(2):123~137.
[29] Woo S, Oh K-W, Two-Dimensional BVI Revisited Using Unstructured Dynamic Meshes, Proceedings of the American Helicopter Society 58th Annual Forum, 2002.
[30] M. V. Lowson, Focusing of Helicopter BVI Noise, Journal of Sound and Vibration, 1996, 190(3):477~494.
[31] Schmitz F H, Sim B W-C, Radiation and Directionality Characteristics of Helicopter Blade-Vortex Interaction Noise, Journal of the American Helicopter Society, 2003, 48(4): 253~269.
[32] Gopalan G, Schmitz F H, Quasi-Static Flight Path Control of Helicopter Blade Vortex Interaction Noise in a Steady Wind, Journal of the American Helicopter Society, 2007, 52(1):15~23.
[33] Ringler T D, George A R, Steele J B, A Study of Blade-Vortex Interaction Sound Generation and Directionality, Proceedings of the AHS and Royal Aeronautical Society, Technical Specialists' Meeting on Rotorcraft Acoustics/Fluid Dynamics, 1991.
[34] Schmitz F H, Reduction of Blade Vortex Interaction (BVI) Noise Through X-force Control, Journal of the American Helicopter Society, 1998, 43(14): 14~24.
[35] Yu Y H, Rotor Blade Vortex Interaction Noise, Progress in Aerospace Sciences, 2000, 36:97~115.
[36] Chehab M, W?lk J, A Windtunnel Study of X-Force Generators to Reduce Helicopter Blade-Vortex Interaction (BVI) Noise, Proceedings of the AIAA Student Design Conference, 2000.
[37] Schmitz F H, Gopalan G, Sim B-C, Flight Trajectory Management to Reduce Helicopter Blade-Vortex Interaction(BVI) Noise with Head/Tailwind Effects, Proceedings of the 26th European Rotorcraft Forum, 2000.
[38] Kuo B C, Sim B W-C, Schmitz F H, Blade-Vortex Interaction Wave Radiation Patterns of Helicopter Blades With Different Leading-Edge Geometry, Proceedings of the American Helicopter Society 58th Annual Forum, 2002.
[39]王华明,张强,胡章伟等, AS350B2直升机飞行噪声的试验研究,声学学报, 2003, 38(2):177~181.
[40]徐国华,高正,悬停状态下模型旋翼噪声试验的初步研究,空气动力学学报, 1996, 14(1):68~72.
[41]徐国华,高正,直升旋翼旋转噪声的估算,南京航空航天大学学报, 1991, 23(2):20~26.
[42]李启,张强,刘建付,直升机尾桨定常载荷噪声的工程计算方法,南京航空航天大学学报, 2006, 38 (2):136~142.
[43]王华明,陈本现,悬停状态下旋翼旋转噪声的分析,南京航空航天大学学报, 2003, 35(3):273~276.
[44]宋文萍,韩忠华,杨爱明等,旋翼跨声速流动气动噪声的一种高效算法,西北工业大学学报, 2001, 19(4):515~519.
[45]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.
[46]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.
[47]招启军,徐国华,王适存,基于CFD/Kirchhoff方法的直升机旋翼高速脉冲噪声模拟分析,计算物理, 2006, 23(2):137~143.
[48]曹义华,康鹏斌,于子文,旋翼翼型-桨尖涡干扰的数值模拟,航空动力学报, 2003, 18(5):604~607.
[49] Castles W, Durham H L, Distribution of Normal Component of Induced Velocity in Lateral Plane of a Lifting Rotor, NACA TN-3841, 1956.
[50] 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.
[51] Kocurek J D, Tangler J L, A Prescribed Wake Lifting Surface Hover Performance Analysis, Journal of the American Helicopter Society, 1977, 22(1):24~35.
[52]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.
[53] Martin P B, Bhagwat M J, Leishman J G, Visualization of a Helicopter Rotor Wake in Hover, AIAA 9923225, 1999.
[54]王适存主编,直升机空气动力学,航空专业教材编审组, 1983.
[55] Landgrebe A J, An Analytical and Experimental Investigation of Helicopter Rotor Hover Performance and Wake Geometry Characteristics, USA AMRDL TR-71224, 1971.
[56] Shenoy K R, Gray R B, Iterative Lifting Surface Method for Thick Bladed Hovering Helicopter Rotors, Journal of Aircraft, 1981, 18(6): 417~424.
[57]王适存,升力螺旋桨在桨盘上的诱导速度分布,力学学报, 1964, 7(3):211~221.
[58]王适存,徐国华,直升机旋翼空气动力学的发展,南京航空航天大学学报, 2001, 33(3):203~211.
[59] Beddoes T S, A Wake Model for High Resolution Airloads, Proceedings of the International Conference on Rotorcraft Basic Research, 1985.
[60] Landgrebe A J, Prediction of Helicopter Induced Flow Velocities Using the Rotorcraft Wake Ananlysis, Proceedings of the 32nd Annual Forum of the American Helicopter Society, 1976.
[61] Quackenbush T R, Lam C M G, Wachspress D A, et al., Analysis of High Resolution Unsteady Airloads for Helicopter Rotor Blades, Proceedings of the American Helicopter Society 50thAnnual Forum, 1994.
[62] 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.
[63] Sadler S G, Development and Application of a Method for Predicting Rotor Free Wake Positions and Resulting Rotor Blade Air Loads, 1971.
[64] Scully M. P.: A Method of Computing Helicopter Vortex Wake Distortion, Massachusetts Institute of Technology, ASRL TR-138-1, 1967.
[65] 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.
[66] Miller R H, A Simplified Approach to the Free Wake Analysis of a Hovering Rotor, Proceedings of the 7th European Rotorcraft Forum , 1981.
[67] Egolf T A, Sparks S P, A Full Potential Rotor Analysis with Wake Influence Using an Inner-Outer Domain Technique, Proceedings of the 42nd Annual AHS Forum, 1986.
[68] Bliss D B, Dadone L, Wachspress D A, Rotor Wake Modeling for High Speed Applications, Proceedings of the American Helicopter Society 43rd Annual Forum, 1987.
[69] Johnson W, A Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dynamics, NASA TM-81182, 1982.
[70] He C, Lee C S, Chen W, Rotorcraft Simulation Model Enhancement to Support Design, Testing and Operational Analysis, Journal of the American Helicopter Society, 2000, 45(4):284~292.
[71]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.
[72] Crouse, Jr G L, Leishman J G, A New Method for Improved Rotor Free Wake Convergence, Proceedings of the 31st AIAA Aerospace Sciences Meeting and Exhibit, 1993.
[73] Bagai A, Leishman J G, Rotor Free-Wake Modeling Using a Relaxation Technique -Including Comparisons with Experimental Data, Journal of the American Helicopter Society, 1995, 40(3):29~41.
[74] Bhagwat M J, Leishman J G, Rotor Aerodynamics During Maneuvering Flight Using a Time-Accurate Free-vortex Wake , Journal of the American Helicopter Society, 2003, 48(3):143~158.
[75]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):54~59.
[76]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.
[77]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.
[78] Xu G H, Zhao Q J, Gao Z, et al., Prediction of Aerodynamic Interactions of Helicopter Rotor on Its Fuselage, Chinese Journal of Aeronautics, 2002, 15(1):12~17.
[79] He C, Zhao J, Modeling Rotor Wake Dynamics with Viscous Vortex Particle Method, AIAA Journal, 2009, 47(4):902~913.
[80]岳海龙,夏品奇,倾转旋翼机在转换飞行时的旋翼尾迹弯曲非定常动态入流模型,中国科学(E辑:技术科学), 2009, 39(12):1992~2000.
[81] Li P, Chen R, Aerodynamics Analysis of a Rotor Undergoing Maneuvers Using an Efficient Time Marching Free Vortex Method, Proceedings of the 3rd International Basic Research Conference on Rotorcraft Technology, 2009.
[82] Tauszig L, Numerical Detection and Characterization of Blade Vortex Interactions Using a Free Wake Analysis, Master Thesis, Pennsylvania State University, 1998.
[83] Johnson W, Rotorcraft Aerodynamics Models for a Comprehensive Analysis, Proceedings of the 54th AHS Annual Forum, 1998.
[84] Leishman J G, Challenges in Modeling the Unsteady Aerodynamics of Wind Turbines, Proceedings of the 40th AIAA Aerospace Sciences Meeting, 2002.
[85] Martin P B, McAlister K W, Chandrasekhara M S, Dynamic Stall Measurements and Computations for a VR-12 Airfoil with a Variable Droop Leading Edge, Proceedings of the American Helicopter Society 59th Annual Forum, 2003.
[86] Nguyen K, Johnson W, Evaluation of Dynamic Stall Models with UH-60A Airloads Flight Test Data, Proceedings of the American Helicopter Society 54th Annual Forum, 1998.
[87] Hyeonsoo Y, Calculation of Rotor Performance and Loads under Stalled Conditions, Proceedings of the 59th AHS Annual Forum, 2003.
[88] Leishman J G, Beddoes T S, A Semi-Empirical Model for Dynamic Stall, Proceedings of the 42nd AHS Annual Forum, 1986.
[89] Leishman J G, Beddoes T S. A Generalized Model for Unsteady Airfoil Behavior and Dynamic Stall Using the Indicial Method, Proceedings of the 42nd AHS Annual Forum, 1986.
[90] Leishman J G, Validation of Approximate Indicial Aerodynamic Functions for Two-dimensional Subsonic Flow, Journal of Aircraft, 1988, 25(10): 914~922.
[91] Beddoes T S, Onset of Leading Edge Separation Effects under Dynamic Conditions and LowMach Number, Proceedings of the 34th AHS Annual Forum, 1978.
[92] Hilaire A, Carta F O, Fink M R, et al., The Influence of Sweep on the Aerodynamic Loading of a NACA0012 Airfoil, NASA CR-3092 1979.
[93] Leishman J G, Lee D, Baeder J D, A Nonlinear Indicial Method for the Calculation of Unsteady Airloads, Proceedings of the 59th AHS Annual Forum, 2003.
[94] Carlson H W, Mack R J, Studies of Leading Edge Thrust Phenomena, Journal of Aircraft, 17(12): 890~897, 1980.
[95] Leishman J G, Modeling Sweep Effects on Dynamic stall, Journal of the AHS, 1989, 34(3):18~29.
[96] Leishman J G, Principles of Helicopter Aerodynamics, Cambridge University Press, 2000.
[97] Bagai A, Contributions to the Mathematical Modeling of Rotor Flow-Fields Using a Pseudo-Implicit Free-Wake Analysis, PhD thesis, University of Maryland, 1995.
[98]黄水林,纵列式直升机双旋翼气动干扰特性的理论与试验研究,博士学位论文,南京航空航天大学, 2009.
[99] Bhagwat M J, Transient Dynamics of Helicopter Rotor Wakes Using a Time-Accurate Free-Vortex Method, PhD thesis, University of Maryland, 2001.
[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] Bagai A, Leishman J G, Rotor Free-Wake Modeling Using a Pseudo-Implicit Algorithm. Journal of Aircraft, 1995, 32(6):1276~1285.
[103] 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.
[104]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气动干扰计算,空气动力学学报, 2007, 25(3):390~395.
[105]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.
[106] Caradonna F X, Tung C, Experimental and Analytical Studies of a Model Helicopter Rotor in Hover, NASA TM-81232, 1981.
[107] Leishman J G, Bagai A, Fundamental Studies of Rotor Wakes in Low Speed Forward Flight Using Wide-field Shadowgraphy, AIAA Paper 91-3232, 1991.
[108] Scheiman J, A Tabulation of Helicopter Rotor-Blade Differential Pressures, Stress and Motions Measured in Flight, NASA TM-X952, 1964.
[109]徐国华,直升机旋翼噪声分析及估算方法,硕士论文,南京航空学院, 1990.
[110] Dahan C, Gratieux E, Helicopter Rotor Thickness Noise, AIAA-80-1012R, 1980.
[111] Brentner K S, Numerical Algorithms for Acoustic Integrals with Examples for Rotor Noise Prediction, AIAA Journal, 1997, 35(4):625~630.
[112] Brentner K S, Farassat F, Modeling Aerodynamically Generated Sound of Helicopter Rotors, Progress in Aerospace Science, 2003, 39(2-3):83~120.
[113] ?zy?rük Y, Alpmana E, Ahujab V, et al., Frequency-Domain Prediction of Turbofan Noise Radiation, Journal of Sound and Vibration, 2004, 270(4-5):933~950.
[114] Strawn R C, Biswas R, Lyrintzis A S, Helicopter Noise Predictions Using Kirchhoff Methods, Journal of Computational Acoustics 1996, 4(3): 321~339.
[115] Farassat F, Acoustic Radiation from Rotating Blades—the Kirchhoff Method in Aeroacoustics, Journal of Sound and Vibration, 2001, 239(4):785~800.
[116] Singh R K, Transonic Effects on Aerodynamics and Acoustics of Blade-Vortex Interaction, PhD thesis, University of Maryland, 1999.
[117] Kuntz M, Rotor Noise Predictions in Hover and Forward Flight Using Different Aeroacoustic Methods, AIAA 96-1695, 1996.
[118] Sim B W-C, Schmitz F H, Blade-Vortex Interaction (BVI) Noise: Retreating Side Characteristics, Sensitivity to Chordwise Loading and Unsteady Aerodynamics,Proceedings of the American Helicopter Society Aeromechanics Specialists’Meeting, 2000.
[119] Daniel G. O, et al, Rotorcraft Aerodynamic and Aeroacoustic Modelling Using Vortex Particle Methods, Proceedings of the 23rd International Council of the Aeronautical Sciences, 2002.
[120] Caradonna F, Kitapliogiu C, Method for the Prediction of Blade-Vortex Interaction Noise, Proceedings of the American Helicopter Society Technical Specialists’Meeting for Rotorcraft Acoustics and Aerodynamics, 1997.
[121] Purcell T W, CFD and Transonic Helicopter Sound, Proceedings of the 14th European Rotorcraft Forum, 1988.
[122] Landgrebe A F, Bellinger E D, An Investigation of the Quantitative Applicability of Model Helicopter Rotor Wake Patterns Obtained From a Water Tunnel, USAAMRDL TR 71-69, 1971.
[123] Sim B W-C, Near/Far-Field Radiation Characteristics of Advancing Side HelicopterBlade-Vortex Interaction (BVI) Noise, Proceedings of the American Helicopter Society 56th Annual National Forum, 2000.
[124] Nakamura Y, Prediction of Blade-Vortex Interaction Noise from Measured Blade Pressure, Proceedings of the 7th European Rotorcraft and Powered Lift Aircraft Forum, 1981.
[125]超级战斗机突破音障瞬间的精美照片, http://www.chinanews.com.cn/tp/news/2009/05-30/1711959.shtml,2009.
[126] Leishman J G, Sound Directivity Generated by Helicopter Rotors Using Wave Tracing Concepts, Journal of Sound and Vibration, 1999,221(3): 415~441.
[127] Sim B W, Schmitz F H, Acoustic Phasing and Amplification Effects of Single Rotor Helicopter Blade-Vortex Interactions, Proceedings of the American Helicopter Society 55th Annual Forum, 1999.
[128] Sim B W-C, George A R, Yen S J, Blade Vortex Interaction Directivity Studies Using Trace Mach Number, Proceedings of 2nd AHS Aeromechanics Specialists’Conference, 1995.
[129] Sim W-C, Blade-Vortex Interaction Noise Generation and Directionality, PhD thesis, Conell University, 1996.
[130] Hu H, Jordan Jr L A, Beader J D, CFD Investigation of Double-Swept Blade in BVI Noise Reduction, Proceedings of the 9th AIAA/CEAS Aeroacoustics Conference and Exhibit, 2003.
[131] Hoad D R, Evaluation of Helicopter Noise due to Blade-Vortex Interaction for Five Tip Configurations, NASA TM-1608, 1979.
[132]招启军,新型桨尖旋翼流场及噪声的数值模拟研究,博士学位论文,南京航空航天大学, 2005.
[133] Srinivasan G R, Raghavan V, Duque E P N, et al., Flowfield Analysis of Mordern Helicopter Rotors in Hover by Navier-Stokes Method, Proceedings of the 47th Annual Forum of AHS, 1991.
[134] Lim J W, Strawn R C, Computational Modeling of HART II Blade-Vortex Interaction Loading and Wake System, Journal of Aircraft, 2008, 45(3):923~933.
[135] Tamura A, Tsutahara M, Kataoka T, et al., Numerical Simulation of Two-Dimensional Blade-Vortex Interactions Using Finite Difference Lattice Boltzmann Method, AIAA Journal, 2008, 46(9):2235~2245.
[136] Malovrh B, Gandhi F, Sensitivity of Helicopter Blade-Vortex-Interaction Noise and Vibration to Interaction Parameters, Journal of Aircraft, 2005, 42(3): 685~697.
[137] Yu Y H, Tung C, Gallman J, Aerodynamics and Acoustics of Rotor Blade-VortexInteractions,Journal of Aircraft, 1995, 32(5): 970~977.
[138] Tung C, Kube R, Brooks T F, et al, Prediction and Measurement of Blade–Vortex Interaction, Journal of Aircraft, 1998, 35(2): 260~266.
[139] Lee Y-C, An Experimental and Theoretical Study of Helicopter Rotor Noise,PhD thesis, Massachusetts Institute of Technology, 1975.
[140] George A R, Lyrintzis A S, Acoustics of Transonic Blade-Vortex Interactions, AIAA Journal, 1988, 26(7):769~776.
[141] Epstein R J, Rule J A, Bliss D B, Novel Method for Calculating Two-Dimensional Blade Vortex Interaction, AIAA Journal, 1997, 35(5):909~912.
[142] DuVall T, Sim B W, Schmitz F H, Cabin versus Far-Field Blade-Vortex Interaction Noise Level Trends, Proceedings of the AHS Aerodynamics, Acoustics, and Test Evaluation Technical Specialists Meeting, 2002.
[143] Gervais M, Schmitz F H, Tiltrotor BVI Noise Reduction Through Flight Trajectory Management & Configuration Control, Journal of the AHS, 2004, 49(4):436~446.
[144] Heyson H H, Induced Flow Near a Helicopter Rotor: A Review of Present Knowledge, Journal of Aircraft Engineering and Aerospace Technology, 1993, 31(2):40~44.
[145] AbellóJ C, George A, Wake Displacement Modifications to Reduce Rotorcraft Blade–Vortex Interaction Noise, Journal of Aircraft, 2004, 41(2): 290~303.
[146] Burley C L, Brooks T F, Charles B D, et al, Tiltrotor Aeroacoustic Code (TRAC) Prediction Assessment and Initial Comparisons With TRAM Test Data, Proceedings of the 25th European Rotorcraft Forum, 1999.