舰艇水动力噪声的数值分析与拖曳模测试技术研究
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摘要
现代军用舰船声隐身性能的好坏已成为其十分重要的一项指标,而利用各方面的手段有效的预报、降低舰船的水下噪声亦已成为目前海军装备研究的一个重点与难点。水动力噪声是舰船水下噪声中除结构振动噪声、螺旋桨噪声以外的重要噪声成分,它关系到舰艇的自噪声,同时也关系到舰艇的辐射噪声。本文主要研究了舰船水动力噪声的机理性问题,重点讨论了相关模型的涡激噪声,并利用Fluent噪声模块,分别研究了某水下、水面舰船的水动力噪声问题,同时本文还探讨了一种新型的水动力噪声模型测试技术――拖曳模噪声测试技术。
     1.利用典型的二维粘性涡核的衰减规律-奥辛涡模型计算自由空间中点涡粘性衰减过程中的涡演化,在此基础上应用匹配渐近展开法计算其声辐射并进行相应的频谱分析。自由空间中点涡粘性衰减过程中的辐射声场声压仅在扩散初期较为明显,随着时间的推移而快速衰减;其频段分布较窄,主要处于低频段,频谱分布曲线峰值十分明显;点涡粘性扩散外声场的声压及其频谱分布情况与粘性系数有一定的关联,随着粘性系数增加,声压峰值发生时间后移,其量值有增加的趋势,且振动主频段向频率增加方向移动,振动频率范围略有增大。
     2.机翼为工程结构物中的常见附体,其尾涡的演化及其声辐射具有一定的特征。以椭圆翼与三角翼为研究对象,利用匹配渐近展开法,估算其尾涡粘性衰减过程的外声场,并对其进行频谱分析。计算表明翼尾涡面演化过程伴随着声辐射,椭圆翼尾涡面演化过程的声辐射频谱分布与三角翼尾涡面演化声辐射的相类似,均有两个较明显的频段峰值,所不同的是频率位置会有所漂移,即翼型不同,峰值频率位置会有所漂移。
     3.采用SST k -ω两方程湍流模型求解了潜艇三维非定常粘性流场,基于Lighthill声类比理论,对艇体绕流场的噪声进行了数值计算,并对流噪声的近、远场特性进行了数值分析,探讨了噪声与来流攻角、来流速度、模型尺度、雷诺数之间的关系及围壳位置对声辐射的影响。研究表明潜艇绕流场的声辐射大小与流场中的涡量大小相关,涡量越大,声辐射也越大。当存在攻角、有围壳后移等因素,或使流场中最大涡量有所增大时,相应的流场声辐射也有所增大。
     4.采用VOF方法和SST k -ω两方程湍流模型求解了水面舰船三维非定常粘性流场,基于Lighthill声类比理论,对船体绕流场的噪声进行了数值计算,并对流噪声的近、远场特性进行了数值分析,探讨了自由面、流向角及来流速度之间的关系。计算表明:船艉的声辐射要大于船艏,而船舯即横向的声辐射又显著大于船艏艉即纵向的声辐射,水面舰船绕流场的声辐射大小与流场中的涡量大小相关,涡量越大,声辐射也越大。当船体有合适的外形或对附体进行合适的安装,并有效地改善流场特性,使流场中涡量有所减小时,相应的流场声辐射也有所减小。
     5.提出了一种新型的水动力噪声模型测试方法――拖曳模噪声测试技术。利用拖曳模在背景噪声较低的试验环境中进行潜艇水动力噪声测试研究是一种有效的试验研究手段,该方法利用时频分析法将测试所得具有时间通过特性的时域信号映射至时间-频率域,从而凸现信号的频率成分在时间上的变化规律,籍此识别出水动力噪声并对其加以研究。利用拖曳模测试噪声有其突出特点,包括流场模拟真实可靠、测试方案灵活、可有效地识别各噪声源、便于研究低频噪声等,是对传统水动力噪声测试方法的一个有益的补充。本论文利用这套试验方法研究了某水面舰船模型的水动力噪声特性。
It is very important for modern military vessels to have a rather good acoustic performance today, so using the effective means to forecast and reduce ship noise has become a focus with difficulty for Navy's research. Hydrodynamic noise is one of the acoustic components for ship noise besides structural vibration noise and propeller one, it is closely related to the ship's self-noise, and also related to the ship radiated noise. In this paper some basal discussions about the hydrodynamic noise proposed with a focus on the part of vortex-induced noise, business software named Fluent is used to study acoustic characteristics of hydrodynamic noise about a certain surface ship. A new type of hydrodynamic noise model test technique using remote submersible model is also discussed in this paper.
     1. A typical model for the process of point vortex attenuation named Aoxin vortex is used to simulate the viscosity evolution of the two-dimensional point vortex in a free space, the matching expansion method is used for calculating radiation noise and the corresponding spectral analysis is also put out. The radiation noise of the point vortex in a free space is rather obvious only in the initial evolution process, and with the passage of time it attenuates rapidly; its frequency distribution is of the narrow band which is mainly located in low band, the peak of the spectrum distribution curve is very clear. The sound field of point vortex and its spectrum are relevant to the viscosity coefficient. With viscosity increasing, the peak sound pressure occurred with the time shift after, its magnitude will increase, and its main vibration frequency band will move to the direction of frequency increasing, vibration frequency range will slightly increase.
     2. Wing is a common attached body for engineering structures, its evolution of the tail vortex and radiation sound has certain characteristics. Elliptical wing and delta wing are studied respectivly in this paper, the matching expansion method is used to estimate its acoustic field, and the spectral analysis is also put out. It is shown that there is acoustic radiation accompanied by the tail vortex evolution. It is similar for the acoustic spectrum of elliptic wing and delta wing; there are two obvious peak bands for both of them which will drift to different frequency positions corresponding to different airfoils.
     3. The SST k -ωtwo equation turbulence model is used for the unsteady viscous three-dimensional flow simulation of the submarine. Then, based on Lighthill acoustic theory, the numerical calculation of sound field around the hull is put out and its near and far field characteristics are also numerically analyzed. The influence of the attack angle, flow velocity, model scale, Reynolds coefficient is discussed and the influence of the fairwater location to sound field is also considered. With the increasing of the flow vortex, the sound radiation is increase correspond.
     4. The VOF method and SST k -ωtwo equation turbulence model are used for three-dimensional surface warships to simulate their unsteady viscous flow. Then with the help of the Lighthill theory, the acoustic numerical calculation about the hull in near and far field is also carried out. The influence of free surface, current angle and flow velocity is discussed. It is shown that the acoustic radiation about the ship stern is greater than that about the ship bow, and the horizontal acoustic radiation of the mid-ship is significantly greater than that of the bow and stern. With the increasing of the flow vortex, the sound radiation is increase correspond, so the sound field could be improved by the fluid field improvement with better hull shape or properly using attach body.
     5. A new acoustic test technque using remote model has been introduced to study the underwater noise of a ship. The remote model test project could be properly designed for the acoustic signal collecting. With the help of the appropriate data processing method, the acoustic sources could be analyzed successfully. Much valuable work about the fluid noise and propeller noise could be carried on with the help of remote model, and the low frequency noise which is especially interested for its long distance radiating with small attenuation could also be studied in this way. It is a rather good supplement to the traditional fluid model test.
引文
[1] Lighthill,M.J.1952 On sound generated aerodynamically,I.General theory, Proc.R.Soc.Lond. A211,564-587
    [2] Curle.N. 1955 The influence of solid bounderaries on aerodynamic sound.Proc.Roy. London Soc.231A,1187,505-514
    [3] Burton,I.E and Blevins,R.D.1976 Vortex shedding noise from oscillating cylinders. J.Acoust.Soc.,599-606
    [4] Ffowcs,Williams,J.E. and Hawkings,D.L.1969 sound generation by turbulence and surfaces in arbitrary motion. Phil.Trans.Roy.Soc.264A,321-342
    [5] Farassat,F.1977 Discontinuities in Aerodynamics and Aeroacoustics: The concept and application of generalized derivatives,J.Sound and Vib. 55,165-193
    [6] Farassat,F. and Succi,G.P. 1980 A review of propeller discrete frequency noise prediction technology with emphasis on two current method for time domain calculations. J.Sound and Vib. 71,399-419
    [7] Goldstein,M. 1974 Unified approach to aerodynamics sound generation in the presence of sound boundaries.J.Acoust. Soc.Am.56,497-509
    [8] Powell,A. 1964, Theory of Vortex sound.J.Acoust.sco.Am.36,177-195
    [9] Muller,W.J. and Obermeier,F.1987 Vortex sound.IUTAM Symposium on Vortex Motion,Tokyo
    [10] Crighton,D.G.1981 Acoustic as a branch of fluid mechanics J.Fluid Mech.106,261-298
    [11] Howe,M.S.1975b Contributions to the theory of aerodynamic sound,with application to excess jet noise and the theory of the flute.J.Fluid Mech.71,625-673
    [12]Crighton,D.G.1972 Radiation from Vortex filament motion near a half plane,J.Fluid Mech.51,357-362
    [13] Cannell,P.and Ffowcs Williams,J.E.1973 J.Fluid Mech,58.65
    [14] Yates,J.E. and Sandr,G.1975 Bernoulli Enthalpy:A fundamental concept in the theory of sound.AIAA 75,493
    [15] Yates,J.E.1977 Interaction with and Production of sound by vortex flow.AIAA 77,1352
    [16] Obermeier,F.1979 On a new representation of areoacoustic source distribution I.General Theory.II.Two-Dimentional Model Flows.Acoustica 42,58-71
    [17] Goldstein,M.V. 1979 Turbulence generated by interaction of entropy fluctuations with nonuniform mean flow.J.Fluid Mech.93,209-224
    [18] Goldstein,M.V. 1980 The effect of finite turbulence spatial scale on the application ofturbulence by a contracting stream.J.Fluid Mech.98,473-508
    [19] Goldstein,M.V. 1982 High frequency sound emission from moving point multipole sources embedded in arbitrary transversely sheard mean flows.J.Sound and Vib.80,499-521
    [20] Howe,M.S.1984 On the absorption of sound by turbulence and other hydrodynamic flow.IMAJ.Appl.Math.32
    [21] Crow,S.C. 1970 Aerodynamic sound emission as a singular perturbation problem.Stud.Appl.Math.49,21-44
    [22] On the scattering of sound by a rectilinear vortex, M. S. HOWE, Journal of Sound and vibration (1999) 227(5), 1003-1017
    [23] Sound generation by fluid-structure interaction, M.S.How, Computers & structors, Vol.65, No.3, 433-446, 1997
    [24] The interaction of perturbed vortex rings and its sound generation, R.C. K. LEUNG AND N.W. M. KO, Journal of Sound and Vibration 1997, 202(1) 0-16
    [25] Wall-bounded blade-tip vortex interaction noise, R.C.DUNNE AND M.S.HOWE, Journal of Sound and Vibration, 1997, 202(5), 594_507
    [26] Strong interference of sound pressure generated by vortex soliton with axial flow, Kimiaki konno and Yoshi H. Ichikawa, Chaos Solutions & Fractals, Vol.5, No.12. 1995, 2485-2493
    [27] 蔡荣泉,船舶计算流体力学的发展与应用,船舶,2002 年 8 月第 4 期
    [28] 周连第,船舶与海洋工程计算流体力学的研究进展与应用,空气动力学学报,Vo l.16, No.1,M ar.1998
    [29] 李勇,刘志友,安亦然,介绍计算流体力学通用软件——F luent,水动力学研究与进展,Ser. A,Vol 16,No. 2,Jun2, 2001
    [30] 林立,俞孟萨,伏同先,国外水面舰艇声隐身设计及控制技术概况,舰船科学技术, Vol. 27, No. 2,Apr. 2005
    [31] LAGIER Y, STEIEHEN W. Modelling of surface ship noise radiatin using FEM and BEM, UDT′92, 128 -133.
    [32] 田中隆昭,船舶水中辐射噪声的预报和实船试验[ J ]. 石川岛播技报, 1990,30 (3) : 165 - 172.
    [33] ANDRESEN K. Underwater noise from ship hull, Inter Confer. on Noise and Vibration in the Marine Environment, 1995, 1 - 22.
    [34] 河边宽. 船体振动引起的水下声辐射问题计算方法 [C]. 日本造船学会论文集, 1996, 180: 479 - 489.
    [35] MORROW R T, ARMSTRONG G. Ship design to min-mise underwater radiated noise, UDT′92, 1662 - 1676.
    [36] 修理英幸,船舶结构传递噪声的分析技术,日本船用机关学会志, 1990, 25 (9) : 42 - 46.
    [37] MUSHA T. Evaluation of ship radiated noise level from nearfield measurement, Applied Acoustics, 40, 1993, P. 69.
    [38] KOZACZKA E, CZARNECKI S. Investigation of underwater noise radiated by ship in shallow water, UDT′94,502 - 503
    [39] 俞孟萨,吴有生,庞业珍,国外舰船水动力噪声研究进展概述,船舶力学,Vol.11 No.1,Feb.2007
    [40] 何祚镛,水下噪声及其控制技术进展和展望,应用声学,Oct.2001
    [41]水下噪声原理,D.罗斯,海洋出版社,1983
    [42]声学理论基础,何诈镛 赵玉芳,国防工业出版社,1981
    [43] 潜体、附体交界部水动力噪声及抑制方法研究(研究报告),缪国平 刘应中,上海交通大学,2000.10
    [44] Theory of Vortex sound, Powell.A, J.Acoust.Soc.Am.36,177-195
    [45] Lighthill,M.J. On sound generated aerodynamically,I.General theory, Proc.R.Soc.Lond. A211,564-587 1952
    [46] Crighton,D.G. Acoustic as a branch of fluid mechanics J.Fluid Mech.106,261-298,1981
    [47] Obermeier,F. On a new representation of areoacoustic source distribution I.General Theory.II.Two-Dimentional Model Flows.Acoustica 42,58-71 1979
    [48] Howe,M.S. Contributions to the theory of aerodynamic sound,with application to excess jet noise and the theory of the flute.J.Fluid Mech.71,625-673 1975
    [49]Crighton,D.G. Radiation from Vortex filament motion near a half plane,J.Fluid Mech.51,357-362 1972
    [50]Cannell,P.and Ffowcs Williams,J.E. J.Fluid Mech,58-65 1973
    [51] Yates,J.E. and Sandr,G. Bernoulli Enthalpy: A fundamental concept in the theory of sound.AIAA 75,493 1975
    [52] Yates,J.E. Interaction with and Production of sound by vortex flow.AIAA 77,1352 1977
    [53].Goldstein,M.V. Turbulence generated by interaction of entropy fluctuations with nonuniform mean flow.J.Fluid Mech.93,209-224 1979
    [54]Goldstein,M.V. The effect of finite turbulence spatial scale on the application of turbulence by a contracting stream.J.Fluid Mech.98,473-508 1980
    [55] Goldstein,M.V. High frequency sound emission from moving point multipole sources embedded in arbitrary trans versely sheard mean flows.J.Sound and Vib.80,499-521 1982
    [56] Howe,M.S. On the absorption of sound by turbulence and other hydrodynamic flow.IMAJ.Appl.Math.32 1984
    [57] Fluent 6.1 User’s Guide Fluent Inc. Centerra Resource Park
    [58] Influence of low mach number shear flow onacoustic propagation inducts, V. PAGNEUX andB. FROELICH, Journal of Sound and vibration (2001) 246(1), 137-155
    [59] Similarity variables for sound radiation in a uniform flow, C. J. CHAPMAN, Journal of Sound and     [60] The acoustic analogy and the prediction of the noise of rotating blades, F. Farassat and Kenneth S. Brentner, Theoret. Comput. Fluid Dynamics (1998) 10: 155–170
    [61] Shock-wave–vortex interactions: shock and vortex, deformations, and sound production, F. Grasso and S. Pirozzoli, Theoret. Comput. Fluid Dynamics (2000) 13: 421–456
    [62] High order numerical simulation of sound generated by the Kirchhoff vortex, Bernhard Müller, H.C.Yee, Comput Visual Sci 4: 197–204 (2002)
    [63] Mach wave radiation by mixing layers.Part I: Analysis of the sound field, E.J. Avital, N.D. Sandham, and K.H. Luo, Theoret. Comput. Fluid Dynamics (1998) 12: 73–90
    [64] Mach wave radiation by mixing layers.Part II: Analysis of the source field, E.J. Avital, N.D. Sandham, and K.H. Luo, Theoret. Comput. Fluid Dynamics (1998) 12: 91–108
    [65] Evolution of a Lamb quadrupolar vortex, O.U. Velasco Fuentes, Fluid Dynamics Research 26 (2000) 13-33
    [66] Simulating vortex pairs interacting with mixing-layer vortices, M. Kiya , H. Takeo, O. Mochizuki, D. Kudo, Fluid Dynamics Research 24 (1999) 61-79
    [67] Numerical computation of a three-dimensional vortex sheet in a swirl flow, Takashi Sakajo, Fluid Dynamics Research 28 (2001) 423–448
    [68] Longitudinal vortex structure in the flow field produced by a vortex ring impinging on a at plate, Takashi Naitoh, Osamu Banno, Hideo Yamada, Fluid Dynamics Research 28 (2001) 61-74
    [69] Vortex-surface interaction noise: a compendium of worked examples, H. Abou-hussein, A. Debenedictis, N. Harrison, M. Kim, M. A. Rodrigues, F. Zagadou and M. S. Howe, Journal of Sound and vibration (2002) 252(5), 883-918
    [70] Analysis of the sound generated by the paring of two axisymmetric co-rotating vortex rings, R. VERZICCO, Journal of Sound and Vibration 1997,200(3) 236_247
    [71] Acoustic perturbation equations based on flow decomposition via source filtering, R. Ewert,W. Schroder, Journal of Computational Physics 188 (2003) 365–398
    [72] Simulation of acoustic scattering from a trailing edge, B. A. SINGER, K. S. BRENTNER AND D. P. LOCKARD, Journal of Sound and vibration (2000) 230(3), 541-560
    [73] Noise generation of blade-vortex resonance, R. C. K. LEUNGs AND R. M. C. SO, Journal of Sound and vibration (2001) 245(2), 217-237
    [74] Sound radiation from elliptic vortex rings: evolution and interaction, K.W. RYU AND D.J.LEE, Journal of Sound and Vibration 1997 200(3) 281-301
    [75] Interaction between a vortex wake and an immersed rectangular plat, M.K.Bull, A. M.Blazewicz, J. M.Plkels, D. A. Bies, Experimental Thermal and fluid science 1996 12:209-220
    [76] The interaction of perturbed vortex rings and its sound generation. PART II, N. W. M. KO, R. C. K. LEUNGs AND C. C. K. TANG, Journal of Sound and vibration (1999) 228(3), 511-541
    [77] A numerical evaluation of viscous effects on vortex induced noiser, A.IAFRATI, Journal of Sound and Vibration 1996 196(2)018-035
    [78] Trailng edge noise at low mach number, M. S. HOWE, Journal of Sound and vibration (1999) 225(2), 211}238
    [79] Numerical study on the suppression of the vortex induced vibration on the circular cylinder by acoustic excitation, S. Hiejima, T. Nomura, K.Kimura, Y.Fujino, Journal of Wind Engineering and Industrial Aerodynamics, 67& 68, 1997, 325-335
    [80] Mechanisms for sound generation in inviscid two-dimensional vortex interactions, S. K. TANG, Journal of Sound and vibration (2001) 243(5), 823-846
    [81] Basic sound generation mechanisms in inviscid vortex interactions at low Machnumber, S.K. Tang, N.W.M. Ko, Journal of Sound and Vibration 262 (2003) 87–115
    [82] On the scattering of sound by a rectilinear vortex, M. S. HOWE, Journal of Sound and vibration (1999) 227(5), 1003-1017
    [83] Application of vortex sound theory to vortex-pairing noise: sensitivity to errors in flow data, C. Schram , A. Hirschberg, Journal of Sound and Vibration 266 (2003) 1079-1098
    [84] On sound generation from the interaction of two inviscid coaxial vortex rings moving in the same direction, S. K.TANG AND N. W.M. KO, Journal of Sound and Vibration 1995 187(2) 176-209
    [85] Sound generation by fluid-structure interaction, M.S.How, Computers & structors, Vol.65, No.3, 433-446, 1997
    [86] The interaction of perturbed vortex rings and its soud generation, R. C.K.LEUNG AND N. W. M.KO, Journal of Sound and Vibration1997, 202(1) 0-16
    [87] Numerical study of sound emission by 2d regular and chaotic vortex configurations, Omar. M. Knio, Journal of computational physics, 116, 1995, 226-246
    [88] Influence of separation on sound generated by vortex-step interaction, M. S. HOWE, Journal of Fluids and Structures (1997) 11, 857-872
    [89] Numerical investigation of the interaction of coaxial vortex rings, M. Konstantinov, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 7 No. 2/3, 1997, pp. 120-140
    [90] Vorticity and the theory of aerodynamic sound, M. S. HOWE, Journal of Engineering Mathematics 41: 367–400, 2001.
    [91] Sound generated by a vortex interacting with a rib-stiffened elastic plat, P.L. SHAH ANDM.S.HOWE, Journal of Sound and Vibration 19960 197(2) 103-115
    [92] Vortex shedding of bluff bodies: a review , M. MATSUMOTO, Journal of Fluids and Structures (1999) 13, 791-811
    [93] The interaction of perturbed vortex rings and its sound generation, R.C. K. LEUNG AND N.W. M. KO, Journal of Sound and Vibration 1997, 202(1) 0-16
    [94] Wall-bounded blade-tip vortex interaction noise, R.C.DUNNE AND M.S.HOWE, Journal of Sound and Vibration, 1997, 202(5), 594_507
    [95] Strong interference of sound pressure generated by vortex soliton with axial flow, Kimiaki konno and Yoshi H. Ichikawa, Chaos Solutions & Fractals, Vol.5, No.12. 1995, 2485-2493
    [96] Sound radiation from elliptic vortex rings: evolution and interaction, K,W, RYU and D.J.LEE, Journal of Sound and Vibration 1997, 200(3) 281-301
    [97] The interaction of perturbed vortex rings and its sound generation. part II N. W. M. KO, R. C. K. LEUNGs and C. C. K. TANG, Journal of Sound and vibration (1999) 228(3), 511-541
    [98] Influence of seperation on sound generated by vortex-step interaction, M. S. HOWE, Journal of Fluids and Structures (1997) 11, 857-872
    [99] Trailing edge noise at low mach number, M. S. HOWE, Journal of Sound and vibration (1999) 225(2), 211-238
    [100] Mechanisms for sound generation in inviscid two-dimensional vortex interaction, S. K. TANG, Journal of Sound and vibration (2001) 243(5), 823-846
    [101] Unsteady lift and sound produced by an airfoil in a turbulent boundary layer, M. S. HOWE, Journal of Fluids and Structures (2001) 15, 207-225
    [102] Motion of quantized vortices as elementary objects, Uwe R. Fischer, Annals of Physics (1999) 278, 62-85
    [103] Streched vortices- the sinews of turbulence; large-Reynolds-number asymptotics, H. K. Moffatt, S. Kida, K. Ohkitani, J. Fluid Mech.(1994), Vol.259, 241-264
    [104] Emergence and evolution of triangular vortices, G. F. Carnevale, R. C. Kloosterziel, J. Fluid Mech.(1994), Vol.259, 305-331
    [105] Nonlinear acoustics in non-uniform infinite and finite layers, W.Ellermeier, J. Fluid Mech.(1994), Vol.257, 183-200
    [106] Topological vortex dynamics in axisymmetric viscous flow, Mogens V. Melander, Fazle Hussain, J. Fluid Mech.(1994), Vol.260, 57-80
    [107] The scattering of sound waves by a vortex: numerical simulations and analytical solution, Tim Colonius, Sanjiva. Lele Parviz Moin, J. Fluid Mech.(1994), Vol.260, 271-298
    [108]涡运动理论,童秉纲 尹协远 朱克勤,中国科技大学出版社,1994
    [109]田军, 薛群基. 水动力试验和流噪声测试[J]. 实验力学, 1997, 12(3): 411-415.
    [110]罗柏华, 刘宇陆. 湍流边界层流场与噪声实验研究[J]. 实验力学, 2001, 16(4):378-386.
    [111]李福新. 回转体流噪声相似律的实验研究[J]. 流体力学实验与测量, 1999, 13(4): 14-18.
    [112]Arakeri V H. Studies on Scaling of Flow Noise Received at the Stagnation Point of Axisymmetric Body[J]. Journal of Sound and Vibration, 1991, 146: 449-462.
    [113]李福新. 回转体驻点处的流噪声相似律[J]. 西北工业大学学报, 2000, 18(2): 221-224.
    [114]孙晓峰, 周盛. 气动声学[M]. 北京: 国防工业出版社, 1994. 18-24.
    [115]何谟钦,王锡良,沈弘萃,等.潜艇遥控自航模螺旋桨噪声测量分析方法[J].船舶力学,2001,5(1):55-61
    [116] 王之程,陈宗歧,等.舰船噪声测量与分析[M].北京:国防工业出版社,2004
    [117] Sanjit K. Mitra. 数字信号处理[M]. 北京: 电子工业出版社,2005
    [118] 毕毅,王波,水下自航模型无线长波遥控系统,船舶工程,2002.6
    [119] 王波,毕毅,水声式自航模运动轨迹实时测量系统,船舶工程,2003.2
    [120] 王 波 , 毕 毅 , 李 和 平 . 潜 艇 自 航 模 水 下 长 波 遥 控 系 统 [J]. 海 军 工 程 大 学 学报,2007,19(2):17-20