WANG Chunxu, WU Chongjian, CHEN Lejia, QIU Changlin, XIONG Jishi. A comprehensive review on the mechanism of flow-induced noise and related prediction methods[J]. Chinese Journal of Ship Research, 2016, 11(1): 57-71. doi: 10.3969/j.issn.1673-3185.2016.01.008
Citation: WANG Chunxu, WU Chongjian, CHEN Lejia, QIU Changlin, XIONG Jishi. A comprehensive review on the mechanism of flow-induced noise and related prediction methods[J]. Chinese Journal of Ship Research, 2016, 11(1): 57-71. doi: 10.3969/j.issn.1673-3185.2016.01.008

A comprehensive review on the mechanism of flow-induced noise and related prediction methods

doi: 10.3969/j.issn.1673-3185.2016.01.008
  • Received Date: 2015-06-19
  • Publish Date: 2016-02-08
    © 2016 The Authors. Published by Editorial Office of Chinese Journal of Ship Research. Creative Commons License
    This is an Open Access article distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • In this paper, a comprehensive review is presented on the mechanism of flow-induced noise and the related prediction methods. The review consists of four aspects: noise of submerged jets, Turbulent Boundary Layer(TBL)noise, rotor noise, and flow over cavities. The mechanism and applicability of noise prediction in the field of engineering using Lighthill acoustic analogy, Kirchhoff formulation, and the theory of vortex sound are explained in detail. Furthermore, numerical simulation methods of flow-induced noise are summarized. Specifically, Lighthill acoustic analogy presumes the noise source to be known in advance, which simplifies its engineering practice; nevertheless, it is defective to describe the exact interaction be-tween flow and sound. Meanwhile, any sound field could be calculated through Kirchhoff approach without source details, but the calculation in the near-field region directly affects the overall precision of the noise field. Finally, profound research on the interaction between vortex and potential flow indicates that the theo-ry is promising when it comes to the production and transformation of acoustic energy. In this case, free field flow noise is presented in quadruple form, while it is presented in dipole form when hard wall bound-ary exists including operating screws, which serves as a much more effective sound source.
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  • [1]
    LIGHTHILL M J. On sound generated aerodynamically. Ⅰ. general theory[J]. Proceedings of the Royal Society of London(Series A),1952,211(1107):564-587.
    [2]
    LIGHTHILL M J. On sound generated aerodynamical-ly. Ⅱ. turbulence as a source of sound[J]. Pcoceed-ings of the Royal Society of London(Series A),1954, 222(1148):1-32.
    [3]
    王春旭. 水下湍射流及壁面湍流噪声预报方法[D]. 武汉:华中科技大学,2009.
    [4]
    POWELL A. Theory of vortex sound[J]. The Journal of Acoustic Society of America,1964,32(8):982-990.
    [5]
    HOWE M S. Contributions to the theory of aerodynam-ic sound,with application to excess jet noise and the theory of the flute[J]. Journal of Fluid Mechanics, 1975,71(4):625-673.
    [6]
    COLONIUS T,LELE S K. Computational aeroacous-tics:progress on nonlinear problems of sound genera-tion[J]. Progress in Aerospace Science,2004,40(6): 345-416.
    [7]
    WANG M,FREUND J B,LELE S K. Computational prediction of flow-generated sound[J]. Annual Review of Fluid Mechanics,2006,38:483-512.
    [8]
    CROW S C. Aerodynamic sound emission as a singular perturbation problem[J]. Studies in Applied Mathemat-ics,1970,49(1):21-46.
    [9]
    WANG M,LELE S K,MOIN P. Sound radiation during local laminar breakdown in a low-Mach-number boundary layer[J]. Journal of Fluid Mechanics,1996, 319:197-218.
    [10]
    AVITAL E J,SANDHAM N D,LUO K H. Calculation of basic sound radiation of axisymmetric jets by direct numerical simulations[J]. AIAA Journal,1999,37 (2):161-168.
    [11]
    LILLEY G M. On the noise from jets: AGARD CP-131[R].[S.l.:s.n.],1974
    [12]
    RIBNER H S. Perspectives on jet noise[J]. AIAA Journal,1981,19(12):1513-1526.
    [13]
    GOLDSTEIN M E. A generalized acoustic analogy[J]. Journal of Fluid Mechanics,2003,488:315-333.
    [14]
    COLONIUS T,LELE S K,MOIN P. Sound generation in a mixing layer[J]. Journal of Fluid Mechanics, 1997,330:375-409.
    [15]
    LYRINTZIS A S. Review:the use of Kirchhoff's meth-od in computational aeroacoustics[J]. Journal of Flu-ids Engineering,1994,116(4):665-676.
    [16]
    MORGANS R P. The Kirchhoff formula extended to a moving surface[J]. Philosophical Magazine,1930,55 (9):141-161.
    [17]
    FFOWCS-WILLIAMS J E,HAWKINGS D L. Sound generation by turbulence and surfaces in arbitrary mo-tion[J]. Philosophical Transactions of the Royal Soci-ety A:Mathematical,Physical and Engineering Sci-ences,1969,264(1151):321-342.
    [18]
    FARASSAT F,MYERS M K. Extension of Kirchhoff's formula to radiation from moving surfaces[J]. Journal of Sound and Vibration,1988,123(3):451-460.
    [19]
    MORINO L. A general theory of unsteady compress-ible potential aerodynamics:NASA CR-2464 [R].[S.l.:s.n.],1974.
    [20]
    MORINO L. Mathematical foundations of integral methods[M]/MORINO L. Computational methods in potential aerodynamics. Berlin:Springer,1985.
    [21]
    MORINO L,TSENG K. A general theory of unsteady compressible potential flows with applications to aero-planes and rotors[M]/BANERJEE P K,MORINO L. Developments in boundary element methods. Barking UK:Elsevier Applied Science Publisher,1990.
    [22]
    DOAK P E. Analysis of internally generated sound in continuous materials:3. The momentum potential field description of fluctuating fluid motion as a basis for a unified theory of internally generated sound[J]. Journal of Sound and Vibration,1973,26(1):91-120.
    [23]
    HOWE M S. On the absorption of sound by turbu-lence and other hydrodynamic flow[J]. Journal of Ap-plied Mathematics and Mechanics, 1984, 84: 187-209.
    [24]
    YATES J E. Interaction with and production of sound by votex flow[J/OL]. AIAA,1977. [2015-05-30].http://arc.org/doi/abs/10.2514/6.1977-1352.
    [25]
    OBERMEIER F. On a new representation of aero-acoustics source distribution:two-dimentional model flows[J]. Acoustica,1979,42:58-71.
    [26]
    GOLDSTEIN M E. High frequency sound emission from moving point multipole sources embedded in ar-bitrary transversely sheared mean flows[J]. Journal of Sound and Vibration,1982,80(4):499-522.
    [27]
    PARKER R. Acoustic resonances and blade vibration in axial flow compressors[J]. Journal of Sound and Vi-bration,1984,92(4):529-539.
    [28]
    AHUJA K,BURRIN R H. Control of flow separation by sound[M]. Williamsburg,Virginia:AIAA paper, 1984.
    [29]
    MARCHMAN Ⅲ J F,SUMANTRAN V,SCHAEFER C G. Acoustic and turbulence influences on stall hys-teresis[J]. AIAA Journal,1987,2(1):50-51.
    [30]
    WU J Z,VAKILI A D,WU J M. Review of the physics of enhancing vortex lift by unsteady excitation[J]. Progress in Aerospace Sciences,1991,28(2): 73-131.
    [31]
    GINEVSKY A S,VLASOV Y V,KARAVOSOV R K. Acoustic control of turbulent jets[M]. Berlin:Spring-er-Verlag,2004.
    [32]
    GOLDSTEIN M E. Aeroacoustics of turbulent shear flows[J]. Annual Review of Fluid Mechanics,1984, 16:263-285.
    [33]
    局鸿宾,沈孟育. 计算气动声学的问题、方法与进展[J]. 力学与实践,1995,17(5):1-10.
    [34]
    局鸿宾,钟芳源,沈孟育.涡、声干扰研究的某些进展[J]. 力学进展,1997,27(3):358-371.

    JU Hongbin,ZHONG Fangyuan,SHEN Mengyu. Some advances in research on vortex and sound inter-action[J]. Advances in Mechanics,1997, 27(3): 358-371.
    [35]
    TAM C K W,GOLEBIOWSKI M,SEINER J M. On the two components of turbulent mixing noise from su-personic jets[C]/The 2nd State College Aeroacous-tics Conference. Pennsylvania, United States,1996: 6-8.
    [36]
    POWELL A. Aerodynamic noise and the plane bound-ary[J]. The Journal of the Acoustical Society of Amer-ica,1960,32(8):217-236.
    [37]
    FFOWCS-WILLIAMS J E,KEMPTON A J. The noise from the large-scale structure of a jet[J]. Journal of Fluid Mechanics,1978,84(4):673-694.
    [38]
    HUERRE P,CRIGHTON D G. Sound generation by instability waves in a low Mach number jet[C]/The 8th Aeroacoustics Conference of American Institute of Aeronautics and Astronautics . Atlanta,GA,1983.
    [39]
    MANKBADI R,LIU J T C. Sound generated aerody-namically revisited:large-scale structures in a turbu-lent jet as a source of sound[J]. Philosophical Trans-actions of the Royal Society(Series A),1984,311 (15/16):183-217.
    [40]
    孙江龙. 绕潜艇三维厚边界层计算和二维自由面波动研究[D]. 武汉:华中科技大学,2006.
    [41]
    CURLE N. The influence of solid boundaries upon aerodynamic sound[J]. Proceedings of the Royal Soci-ety of London (Series A),1955,231(1187): 505-514.
    [42]
    FFOWCS-WILLIAMS J E,HALL L H. Aerodynamic sound generation by turbulent flow in the vicinity of a scattering half plane[J]. Journal of Fluid Mechanics, 1970,40(4):657-670.
    [43]
    WANG M,MOIN P. Computation of trailing-edge flow and noise using large-eddy simulation[J]. AIAA Journal,2000,38(12):2201-2209.
    [44]
    HOWE M S. Trailing edge noise at low Mach numbers[J]. Journal of Sound and Vibration,1999,225(2): 211-238.
    [45]
    LOWSON M V. The sound field for singularities in motion[J]. Proceedings of the Royal Society(Series A),1965,286(1407):559-572.
    [46]
    LOWSON M V,OLLERHEAD J B. A theoretical study of helicopter rotor noise[J]. Journal of Sound and Vibration,1969,9(2):197-222.
    [47]
    LOWSON M V. Theoretical analysis of compressor noise[J]. The Journal of the Acoustical Society of America,1970,47:371-385.
    [48]
    GOLDSTEIN M. Unified approach to aerodynamic sound generation in the presence of solid boundaries[J]. The Journal of the Acoustical Society of America, 1974,56(2):497-509.
    [49]
    HOWE M S. The damping of sound by wall turbulent shear layers[J]. The Journal of the Acoustical Society of America,1995,98(3):1723-1730.
    [50]
    SHARIFF K,WANG M. A numerical experiment to determine whether surface shear-stress fluctuations are a true sound source[J]. Physics of Fluids,2005, 17(10):105-107.
    [51]
    HU Z W,MORFEY C L,SANDHAM N D. Sound radi-ation in turbulent channel flows[J]. Journal of Fluid Mechanics,2003,475:269-302.
    [52]
    俞孟萨,吴有生,庞业珍. 国外舰船水动力噪声研究进展概述[J]. 船舶力学,2007,11(1):152-158.

    YU Mengsa,WU Yousheng,PANG Yezhen. A review of progress for hydrodynamic noise of ships[J]. Jour-nal of Ship Mechanics,2007,11(1):152-158.
    [53]
    KRAICHNAN R H. Pressure fluctuations in turbulent flow over a flat plate[J]. The Journal of the Acousti-cal Society of America,1956,28(3):378-390.
    [54]
    CORCOS G M. The structure of the turbulent pressure field in boundary-layer flows[J]. Journal of Fluid Me-chanics,1964,18(3):353-378.
    [55]
    CORCOS G M. The resolution of turbulent pressures at the wall of a boundary layer[J]. Journal of Sound and Vibration,1967,6(1):59-70.
    [56]
    FFOWCS-WILLIAMS J E. Boundary-layer pressures and the Corcos model:a development to incorporate low-wavenumber constraints[J]. Journal of Fluid Me-chanics,1982,125:9-25.
    [57]
    CHASE D M. Modeling the wavevector-frequency spectrum of turbulent boundary layer wall pressure[J]. Journal of Sound and Vibration,1980,70(1): 29-67.
    [58]
    CHASE D M. The character of the turbulent wall pres-sure spectrum at subconvective wavenumbers and a suggested comprehensive model[J]. Journal of Sound and Vibration,1987,112(1):125-147.
    [59]
    MARTIN N C,LEEHEY P. Low wavenumber wall pressure measurements using a rectangular membrane as a spatial filter[J]. Journal of Sound and Vibration, 1977,52(1):95-120.
    [60]
    HOWE M S. The turbulent boundary-layer roughwall pressure spectrum at acoustic and subconvective wave numbers[J]. Proceedings of Royal Society of London(Series A),1988,415(1848):141-161.
    [61]
    SMOL'YAKOV A V,TKACHENKO V M. Measure-ment of turbulent fluctuations[M]/BRADSHAW P. The measurement of turbulent fluctuations. Berlin: Springer,1983:46-128.
    [62]
    MELLEN R H. On modeling convective turbulence[J]. The Journal of the Acoustical Society of America, 1990,88(6):2891-2893.
    [63]
    DHANAK M R. Turbulent boundary layer on a circu-lar cylinder:the low-wavenumber surface pressure spectrum due to a low-Mach-number flow[J]. Jour-nal of Fluid Mechanics,1988,191:443-464.
    [64]
    DOWLING A P. Flow-acoustic interaction near a flex-ible wall[J]. Journal of Fluid Mechanics,1983,128: 181-198.
    [65]
    PHILLIPS O M. The intensity of Aeolian tones[J]. Journal of Fluid Mechanics,1956,1:607-624.
    [66]
    ROSS D. Vortex-shedding sound of propellers: AD0435764[R]. 1964-03-16.
    [67]
    ROSS D. Mechanics of underwater noise[M]. Oxford: Pergamon Press,1976.
    [68]
    KEMP N H,SEARS W R. Aerodynamic interference between moving blade rows[J]. Journal of the Aero-nautical Sciences,1953,20(9):585-597.
    [69]
    KEMP N H,SEARS W R. The unsteady forces due to viscous wakes in turbomachines[J]. Journal of the Aeronautical Sciences,1955,22(7):478-483.
    [70]
    SHARLAND I J. Sources of noise in axial flow fans[J]. Journal of Sound and Vibration,1964,1(3): 302-322.
    [71]
    LOWSON M V. Reduction of compressor noise radia-tion[J]. The Journal of the Acoustical Society of America,1968,43(1):37-50.
    [72]
    HANSON D B. Spectrum of rotor noise caused by in-let guide vane wakes[J]. The Journal of the Acousti-cal Society of America,1974,55(6):1247-1251.
    [73]
    朱锡清,吴武生. 水下高速航行体对转螺旋桨线谱噪声预报研究[J]. 声学学报,1998,23(2): 123-133.

    ZHU Xiqing,WU Wusheng. Prediction of line-spec-trum noise induced by high speed vehicle counter-ro-tation propellers in water[J]. Acta Acustica,1998,23 (2):123-133.
    [74]
    朱锡清,吴武生. 螺旋桨负荷噪声研究[J]. 声学学报,1999,24(3):259-268.

    ZHU Xiqing,WU Wusheng. Prediction of marine pro-peller loading noise[J]. Acta Acustica,1999,24(3): 259-268.
    [75]
    朱锡清,唐登海,孙红星,等. 船舶螺旋桨低频噪声研究[J]. 船舶力学,2000,4(1):50-55.
    [76]
    孙红星,朱锡清. 螺旋桨离散谱噪声计算研究[J]. 船舶力学,2003,7(4):105-109.

    SUN Hongxing,ZHU Xiqing. Study on discrete noise induced by marine propeller[J]. Journal of Ship Me-chanics,2003,7(4):105-109.
    [77]
    HANSON D B. Near-field frequency-domain theory for propeller noise[J]. AIAA Journal,1985,23(4): 499-504.
    [78]
    杨兵,王同庆. 螺旋桨定常载荷噪声频域计算的新方法[C]/第十届船舶水下噪声学术讨论会论文集. 无锡:中国造船工程学会船舶力学学术委员会, 2005.
    [79]
    ABRAHAMSSON M,JOHANSSON M. Analysis of pressure pulses generated in a waterjet propulsion unit[D]. Sweden:Chalmers University of Technology, 1998.
    [80]
    KAJI S,OKAZAKI T. Generation of sound by ro-tor-stator interaction[J]. Journal of Sound and Vibra-tion,1970,13(3):281-307.
    [81]
    MANI R. Discrete frequency noise generation from an axial flow fan blade row[J]. Journal of Basic Engi-neering,1970,92(1):37-43.
    [82]
    LIPSTEIN N J,MANI R. Experimental investigation of discrete frequency noise generated by unsteady blade forces[J]. Journal of Basic Engineering,1970, 92(1):155-164.
    [83]
    HETHERINGTON R. Compressor noise generated by fluctuating lift resulting from rotor-stator interaction[J]. AIAA Journal,1963,1(2):473-474.
    [84]
    WRIGHT S E. The acoustic spetrum of axial flow ma-chines[J]. Journal of Sound and Vibration,1976,45 (2):165-223.
    [85]
    SEARS W R. Some aspects of non-stationary airfoil theory and its practical application[J]. Journal of the Aeronautical Sciences,1941,8(3):104-108.
    [86]
    TYLER J M,SOFRIN T G. Axial flow compressor noise studies[R/OL].(1962-01-01)[2015-04-23]. http://papers.sae.org/620532/. doi: 10.4271/620532.
    [87]
    BENZAKEIN M. Fan /compressor noise research: AD-740513.[R].[S.l.:s.n.],1971.
    [88]
    NAMBA M. Three-dimensional analysis of blade force and sound generation for an annular cascade in distorted flows[J]. Journal of Sound and Vibration, 1977,50(4):479-508.
    [89]
    KOBAYASHI H. Three dimensional effects on pure tone fan noise due to inflow distortion[C]/AIAA 11th Fluid and Plasma Dynamics Conference. Seattle, Washington,1978.
    [90]
    ROCKWELL D,NAUDASCHER E. Review-self-sus-taining oscillations of flow past cavities[J]. Journal of Fluids Engineering,1978,100(2):152-165.
    [91]
    COLONIUS T. An overview of simulation,modeling, and active control of flow acoustic resonance in open cavities[C]/The 39th Aerospace Sciences Meeting and Exhibit. Reno,NV:2001:8-11,21.
    [92]
    ROSSITER J E. Wind-tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds:RAE 64037[R]. 1964-10-31.
    [93]
    LAFON P,CAILLAUD S,DEVOS J P,et al. Aero-acoustical coupling in a ducted shallow cavity and flu-id/structure effects on a steam line[J]. Journal of Flu-ids and Structures,2003,18(6):695-713.
    [94]
    BILANIN A J,COVERT E. Estimation of possible ex-citation frequencies for shallow rectangular cavities[J]. AIAA Journal,1973,11(3):347-351.
    [95]
    FAURE T M,ADRIANOS P,LUSSEYRAN F,et al. Visualizations of the flow inside an open cavity at me-dium range Reynolds numbers[J]. Experiments in Fluids,2007,42(2):169-184.
    [96]
    HASSAN M E,LABRAGA L,KEIRSBULCK L. Aero-acoustic oscillations inside large deep cavities[C]/JACOBS P,MCINTYRE T,CLEARY M,et al. 16th Australasian Fluid Mechanics Conference (AFMC).Queensland,Australia,2007.
    [97]
    MEGANATHAN A J,VAKILI A D. An experimental study of open cavity flows at low subsonic speeds[C]/The 40th AIAA Aerospace Sciences Meeting & Exhibit,2002.
    [98]
    FRANKE M E,CARR D L. Effect of geometry on open cavity flow-induced pressure oscillations[C]/AIAA Second Aero-Acoustics Conference. Hampton, Virginia:AIAA,1975:75-492.
    [99]
    KOMERATH N M,AHUJA K K,CHAMBERS F W. Prediction and measurement of flows over cavities—a survey[C]/Proceedings of the AIAA 25th Aerospace Sciences Meeting. Reno,Nevada,1987.
    [100]
    CHOKANI N. Flow induced oscillations in cavities— a critical survey:DGLR/AIAA 92-02-159[R].[S. l.:s.n.]1992.
    [101]
    罗柏华,胡章伟. 流体诱导空腔振荡及其声激励抑制的试验研究[J]. 南京航空航天大学学报,1996, 28(3):331-336.

    LUO Baihua,HU Zhangwei. Experimental study of flow induced cavity oscillation and its suppression by sound excitation[J]. Transactions of Nanjing Uni-versity of Aeronautics & Astronautics,1996,28(3): 331-336.
    [102]
    COLONIUS T. Modeling artificial boundary condi-tions for compressible flow[J]. Annual Review of Fluid Mechanics,2004,36:315-345.
    [103]
    MITCHELL B E,LELE S K. MOIN P. Direct compu-tation of the sound from a compressible co-rotating vortex pair[J]. Journal of Fluid Mechanics,1995, 285:181-202.
    [104]
    INOUE O,HATTORI Y,SASAKI T. Sound genera-tion by coaxial collision of two vortex rings[J]. Jour-nal of Fluid Mechanics,2000,424:327-365.
    [105]
    RAN H Y,COLONIUS T. Numerical simulation of sound radiated from a turbulent vortex ring[C]/The 10th AIAA/CEAS Aeroacoustics Conference,2004: 2004-2918.
    [106]
    FREUND J B,LELE S K,MOIN P. Numerical simu-lation of a Mach 1.92 turbulent jet and its sound field[J]. AIAA Journal,2000,38(11):2023-2031.
    [107]
    FREUND J B. Noise sources in a low-Reyn-olds-number turbulent jet at Mach 0.9[J]. Journal of Fluid Mechanics,2001,438:277-305.
    [108]
    MOIN P. Advances in large eddy simulation method-ology for complex flows[J]. International Journal of Heat and Fluid Flow,2002,23(5):710-720.
    [109]
    BLAKE W K. A statistical description of pressure and velocity fields at the trailing edges of a flat strut: ADA028771[R].[S.l.:s.n.],1975.
    [110]
    WANG M,MOREAU S,IACCARINO G,et al. LES prediction of wall-pressure fluctuations and noise of a low-speed airfoil[J]. International Journal of Aero-ZHU Xiqing,TANG Denghai,SUN Hongxing,et al. Study of low frequency noise induced by propeller[J]. Journal of Ship Mechanics,2000,4(1):50-55.
    [111]
    BOGEY C,BAILLY C,JUVÉ D. Noise investigation of a high subsonic,moderate Reynolds number jet using a compressible large eddy simulation[J]. The-oretical and Computational Fluid Dynamics,2003, 16(4):273-297.
    [112]
    BOGEY C,BAILLY C. Decrease of the effective Reynolds number with eddy-viscosity subgrid-scale modeling[J]. AIAA Journal,2005,43(2):437-439.
    [113]
    PIOMELLI U,STREETT C,SARKAR S. On the computation of sound by large-eddy simulations[J]. Journal of Engineering Mathematics,1997,32(2/3): 217-236.
    [114]
    SEROR C,SAGAUT P,BAILLY C,et al. Sub-grid-scale contribution to noise production in decay-ing isotropic turbulence[J]. AIAA Journal,2000,38 (10):1795-1803.
    [115]
    HE G W,WANG M,LELE S K. On the computation of space-time correlations by large-eddy simulation[J]. Physics of Fluids,2004,16(11):3859-3867.
    [116]
    孟堃宇. 基于大涡模拟的潜艇脉动压力与流噪声性能数值计算[D]. 上海:上海交通大学,2011.
    [117]
    张允,傅慧萍,缪国平. 基于大涡模拟的开孔潜体流噪声数值模拟[J]. 上海交通大学学报,2011,45 (12):1868-1873.

    ZHANG Yun, FU Huiping, MIAO Guoping. LES-based numerical simulation of flow noise for submerged body with cavities[J]. Journal of Shang-hai Jiaotong University,2011,45(12):1868-1873.
    [118]
    DEARDORFF J W. A numerical study of three-di-mensional turbulent channel flow at large Reynolds numbers[J]. Journal of Fluid Mechanics,1970,41 (2):453-480.
    [119]
    WANG M,MOIN P. Dynamic wall modeling for large-eddy simulation of complex turbulent flows[J]. Physics of Fluids,2002,14(7):2043-2051.
    [120]
    SPALART P R,JOU W H,STRELETS M,et al. Comments on the feasibility of LES for wings and on a hybrid RANS/LES approach[C]/Advances in DNS/LES,Conference of 1st AFOSR on DNS/LES. Columbus:Greyden Press,1997.
    [121]
    HEDGES L S,TRAVIN A K,SPALART P R. De-tached-eddy simulations over a simplified landing gear[J]. Journal of Fluids Engineering,2002,124 (2):413-423.
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