WEI B B, GAO Y W, SUN B, et al. Statistical characteristics analysis of fluctuating pressure in airfoil boundary layer[J]. Acta Aerodynamica Sinica, 2022, 40(6): 129-137(in Chinese).

ZHAO K, LIANG J B, BELYAEV I, et al. Review of civil airplane landing gear noise study and its control approaches[J]. Acta Aeronautica et Astronautica Sinica, 2022, 43(8): 137-173.

ZHAO K, OKOLO P, NERI E, et al. Noise reduction technologies for aircraft landing gear-a bibliographic review[J]. Progress in Aerospace Sciences, 2020, 112: 100589. DOI: 10.1016/j.paerosci.2019.100589

CHEN C J, HE H Y, SHAO Y L. Extraction of fluctuating pressure on high-speed train surface based on wavelet transform[J]. Journal of Southwest Jiaotong University, 2015, 50(3): 472-477(in Chinese).

ZHANG X L, ZHANG N, WU B S. Computation of turbulent wall pressure fluctuation and its wavenumber-frequency spectrum using large eddy simulation[J]. Journal of Ship Mechanics, 2014, 18(10): 1151-1164(in Chinese).

XU J Q, ZHOU Z L, MEI Z Y. The characteristics and mechanisms of turbulent pressure induced self-noise of the elastomer layer attached stiffened plate[J]. Acta Acustica, 2021, 46(1): 143-160(in Chinese).

LYU S J, GAO Y, LIU J, et al. Application analysis on the wavenumber-frequency spectrum of pressure excited by a turbulent boundary layer on the wall of an underwater test vehicle[J]. Chinese Journal of Ship Research, 2020, 15(Supp 1): 55-60 (in Chinese). doi: 10.19693/j.issn.1673-3185.01581

ZUO K C, CHEN P, WANG Z, et al. Research status of aircraft interior noise[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(8): 2370-2384(in Chinese).

CASALINO D, DIOZZI F, SANNINO R, et al. Aircraft noise reduction technologies: a bibliographic review[J]. Aerospace Science and Technology, 2008, 12(1): 1-17. DOI: 10.1016/j.ast.2007.10.004

FOLEY A W, KEITH W L, CIPOLLA K M. Comparison of theoretical and experimental wall pressure wavenumber-frequency spectra for axisymmetric and flat-plate turbulent boundary layers[J]. Ocean Engineering, 2011, 38(10): 1123-1129. DOI: 10.1016/j.oceaneng.2011.05.001

KEITH W L, CIPOLLA K M. Features of the turbulent wall pressure field on a long towed cylinder[J]. Experiments in Fluids, 2010, 49(1): 203-211. DOI: 10.1007/s00348-010-0841-0

CIPOLLA K M, KEITH W L. Measurements of the wall pressure spectra on a full-scale experimental towed array[J]. Ocean Engineering, 2008, 35(10): 1052-1059. DOI: 10.1016/j.oceaneng.2008.02.006

WILLMARTH W. Space-time correlations and spectra of wall pressure in a turbulent boundary layer[R ] . NASA-MEMO-3-17-59W, 1959. https://ntrs.nasa.gov/api/citations/19980237100/downloads/19980237100.pdf

BLAKE W K, CHASE D M. Wavenumber-frequency spectra of turbulent-boundary-layer pressure measured by microphone arrays[J]. The Journal of the Acoustical Society of America, 1971, 49(3B): 862-877. DOI: 10.1121/1.1912427

SHERMAN C H, KO S H, BUEHLER B G. Measurement of the turbulent boundary layer wave-vector spectrum[J]. The Journal of the Acoustical Society of America, 1990, 88(1): 386-390. DOI: 10.1121/1.400347

KO S H, NUTTALL A H. Analytical evaluation of flush-mounted hydrophone array response to the Corcos turbulent wall pressure spectrum[J]. The Journal of the Acoustical Society of America, 1991, 90(1): 579-588. DOI: 10.1121/1.401232

ABRAHAM B M, KEITH W L. Direct measurements of turbulent boundary layer wall pressure wavenumber-frequency spectra[J]. Journal of Fluids Engineering, 1998, 120(1): 29-39. DOI: 10.1115/1.2819657

ARGUILLAT B, RICOT D, ROBERT G, et al. Measurements of the wavenumber-frequency spectrum of wall pressure fluctuations under turbulent flows[C]//11th AIAA/CEAS Aeroacoustics Conference. Monterey, California: American Institute of Aeronautics and Astronautics, Monterey, California, 2005. doi:10.2514/6.2005-2855

SALZE E, BAILLY C, MARSDEN O, et al. An experimental characterisation of wall pressure wavevector-frequency spectra in the presence of pressure gradients[C]//20th AIAA/CEAS Aeroacoustics Conference. Atlanta, GA, 2014. doi:10.2514/6.2014-2909

SCHRAM C F, VAN DE WYER N. An optimized microphone array for the measurement of turbulent boundary layer wall pressure wavenumber-frequency spectra[C]//2018 AIAA/CEAS Aeroacoustics Conference. Atlanta, Georgia, 2018. doi:10.2514/6.2018-2968

SALZE E, JONDEAU E, PEREIRA A, et al. A new MEMS microphone array for the wavenumber analysis of wall-pressure fluctuations: application to the modal investigation of a ducted low-Mach number stage[C]//25th AIAA/CEAS Aeroacoustics Conference. Delft, The Netherlands, 2019. doi:10.2514/6.2019-2574

MERINO-MARTÍNEZ R, SIJTSMA P, SNELLEN M, et al. A review of acoustic imaging methods using phased microphone arrays[J]. CEAS Aeronautical Journal, 2019, 10(1): 197-230. DOI: 10.1007/s13272-019-00383-4

ZHAO K, ZHANG R P, KOPIEV V, et al. A parametric study of nose landing gear noise in a large-scale aeroacoustic wind tunnel[J]. Applied Acoustics, 2022, 201: 109130. DOI: 10.1016/j.apacoust.2022.109130

ZHAO K, ALIMOHAMMADI S, OKOLO P N, et al. Aerodynamic noise reduction using dual-jet planar air curtains[J]. Journal of Sound and Vibration, 2018, 432: 192-212. DOI: 10.1016/j.jsv.2018.06.036

ROBIN O, MOREAU S, PADOIS T, et al. Measurement of the wavenumber-frequency spectrum of wall pressure fluctuations: spiral-shaped rotative arrays with pinhole-mounted quarter inch microphones[C]//19th AIAA/CEAS Aeroacoustics Conference. Berlin, Germany, 2013. doi: 10.2514/6.2013-2058

HAXTER S, RAUMER H G, BERKEFELD T, et al. Determining flow propagation direction from In-flight array surface pressure fluctuation data[J]. AIAA Journal, 2022, 60(10): 5868-5879. doi: 10.2514/1.j061711

HAXTER S, SPEHR C, HARTMANN M, et al. Improving the performance of aeroacoustic measurements beneath a turbulent boundary layer in a wake flow[C]//20th AIAA/CEAS Aeroacoustics Conference. Atlanta, GA, 2014. doi:10.2514/6.2014-3289

BAHR C J, CATTAFESTA L N. Wavenumber–frequency deconvolution of aeroacoustic microphone phased array data of arbitrary coherence[J]. Journal of Sound and Vibration, 2016, 382: 13-42. DOI:10.1016/j.jsv.2016.06.044

PANG Y Z, YU M. Research on fluctuation pressure test for nonequilibrium turbulence boundary-layer[J]. Journal of Ship Mechanics, 2016, 20(5): 515-522(in Chinese).

ZHAO K, YANG M, ZHANG R P. Two-dimensional dot matrix design method and device for wind tunnel pulsating pressure measurement: CN115575081A[P]. 2023-03-14(in Chinese).

ZHAO X, GUO M, LEI J. Updating of wavenumber-frequency spectrum models by a phased array measurement[J]. Aerospace Science and Technology, 2020, 107: 106273. DOI: 10.1016/j.ast.2020.106273

ZHAO X J, LEI J M. Improved technique for evaluation of wall pressure fluctuations from turbulent boundary layer[J]. AIAA Journal, 2020, 58(8): 3320-3331. DOI: 10.2514/1.j059164

GRAHAM W R. A comparison of models for the wavenumber-frequency spectrum of turbulent boundary layer pressures[J]. Journal of Sound and Vibration, 1997, 206(4): 541-565. DOI: 10.1006/jsvi.1997.1114

MILLER T S, GALLMAN J M, MOELLER M J. Review of turbulent boundary layer models for acoustic analysis[J]. Journal of Aircraft, 2012, 49(6): 1739-1754. DOI: 10.2514/1.c031405

WANG C X, ZENG G W, XU J. A comparative study of models for the wavenumber-frequency spectrum of tbl fluctuation pressure[J]. Chinese Journal of Ship Research, 2011, 6(1): 35-40.

张兆顺, 崔桂香, 许春晓. 湍流理论与模拟[M]. 第2版. 北京: 清华大学出版社, 2017.

LAURENT C, MARY I, GLEIZE V, et al. Rans modeling of a transitional laminar separation bubble on a flat plate with DNS database[C]//40th Fluid Dynamics Conference and Exhibit. Chicago, Illinois, 2010. doi:10.2514/6.2010-4444

PHILLIPS M. On the aerodynamic surface sound from a plane turbulent boundary layer[J]. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences, 1956, 234(1198): 327-335. DOI: 10.1098/rspa.1956.0037

KRAICHNAN R H. Pressure fluctuations in turbulent flow over a flat plate[J]. The Journal of the Acoustical Society of America, 1956, 28(3): 378-390. DOI: 10.1121/1.1908336

BONNESS W K, CAPONE D E, HAMBRIC S A. Low-wavenumber turbulent boundary layer wall-pressure measurements from vibration data on a cylinder in pipe flow[J]. Journal of Sound and Vibration, 2010, 329(20): 4166-4180. DOI: 10.1016/j.jsv.2010.04.010

BLAKE W. Essentials of turbulent wall pressure fluctuations[M]//BLAKE W K. Mechanics of flow-induced sound and vibration, Volume 2. Second Edition. Academic Press, 2017: 81-177. doi: 10.1016/B978-0-12-809274-3.00002-7

EVANS N D, CAPONE D E, BONNESS W K. Low-wavenumber turbulent boundary layer wall-pressure measurements from vibration data over smooth and rough surfaces in pipe flow[J]. Journal of Sound and Vibration, 2013, 332(14): 3463-3473. DOI: 10.1016/j.jsv.2013.01.028

CORCOS G M. Resolution of pressure in turbulence[J]. The Journal of the Acoustical Society of America, 1963, 35(2): 192-199. DOI: 10.1121/1.1918431

CORCOS G M. The structure of the turbulent pressure field in boundary-layer flows[J]. Journal of Fluid Mechanics, 1964, 18(3): 353. DOI: 10.1017/s002211206400026X

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. DOI: 10.1016/0022-460X(67)90158-7

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. DOI: 10.1016/0022-460X(80)90553-2

EFIMTSOV B M. Characteristics of the field of turbulent wall pressure-fluctuations at large Reynolds-numbers[J]. Soviet Physics Acoustics-USSR, 1982, 28(4): 289-292.

WILLIAMS J E F. Boundary-layer pressures and the Corcos model: a development to incorporate low-wavenumber constraints[J]. Journal of Fluid Mechanics, 1982, 125: 9. DOI: 10.1017/s0022112082003218

HWANG Y F, GEIB F E. Estimation of the wavevector-frequency spectrum of turbulent boundary layer wall pressure by multiple linear regression[J]. Journal of Vibration and Acoustics, 1984, 106(3): 334-342. DOI: 10.1115/1.3269199

WITTING J M. A spectral model of pressure fluctuations at a rigid wall bounding an incompressible fluid, based on turbulent structures in the boundary layer[J]. Noise Control Engineering Journal, 1986, 26(1): 28. DOI: 10.3397/1.2827660

CHASE D M. The character of the turbulent wall pressure spectrum at subconvective wavenumbers and a suggested comprehensive model[J]. Journal of Sound and Vibration, 1987, 112(1): 125-147. DOI: 10.1016/S0022-460X(87)80098-6

MELLEN R H. On modeling convective turbulence[J]. The Journal of the Acoustical Society of America, 1990, 88(6): 2891-2893. DOI: 10.1121/1.399695

MELLEN R H. Wave-vector filter analysis of turbulent flow[J]. The Journal of the Acoustical Society of America, 1994, 95(3): 1671-1673. DOI: 10.1121/1.408556[LinkOut]

SMOL’YAKOV A, TKACHENKO V, WOOD J. Model of a field of pseudosonic turbulent wall pressures and experimental data[J]. Soviet Physics: Acoustics, 1991, 37(6): 627-631.

PARCHEN R R. Progress report DRAW: A prediction scheme for trailing edge noise based on detailed boundary layer characteristics[R]. TNO Institute of Applied Physics, HAG-RPT-980023, 1998.

MORIARTY P, GUIDATI G, MIGLIORE P. Prediction of turbulent inflow and trailing-edge noise for wind turbines[C]//11th AIAA/CEAS Aeroacoustics Conference. Monterey, California, 2005. doi: 10.2514/6.2005-2881

SMOL’YAKOV A V. Calculation of the spectra of pseudosound wall-pressure fluctuations in turbulent boundary layers[J]. Acoustical Physics, 2000, 46(3): 342-347. DOI: 10.1134/1.29890

SMOL’YAKOV A V. A new model for the cross spectrum and wavenumber-frequency spectrum of turbulent pressure fluctuations in a boundary layer[J]. Acoustical Physics, 2006, 52(3): 331-337. DOI: 10.1134/S1063771006030146

BULL M K. Wall-pressure fluctuations associated with subsonic turbulent boundary layer flow[J]. Journal of Fluid Mechanics, 1967, 28(4): 719-754. DOI: 10.1017/S0022112067002411

KRAICHNAN R H. Pressure field within homogeneous anisotropic turbulence[J]. The Journal of the Acoustical Society of America, 1956, 28(1): 64-72. DOI: 10.1121/1.1908224

LIGHTHILL M J. On sound generated aerodynamically I. General theory[J]. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences, 1952, 211(1107): 564-587. DOI: 10.1098/rspa.1952.0060

WILLIAMS J E F. Surface-pressure fluctuations induced by boundary-layer flow at finite Mach number[J]. Journal of Fluid Mechanics, 1965, 22(3): 507-519. DOI: 10.1017/S0022112065000939

KLINE S J, REYNOLDS W C, SCHRAUB F A, et al. The structure of turbulent boundary layers[J]. Journal of Fluid Mechanics, 1967, 30(4): 741-773. DOI: 10.1017/S0022112067001740

ROBINSON S K. Coherent motions in the turbulent boundary layer[J]. Annual Review of Fluid Mechanics, 1991, 23: 601-639. DOI: 10.1146/annurev.fl.23.010191.003125

JR BERGERON R F. Aerodynamic sound and the low-wavenumber wall-pressure spectrum of nearly incompressible boundary-layer turbulence[J]. The Journal of the Acoustical Society of America, 1973, 54(1): 123-133. DOI: 10.1121/1.1913553

CHASE D M. Recent modeling of turbulent wall pressure and fluid interaction with a compliant boundary[J]. Journal of Vibration and Acoustics, 1984, 106(3): 328-333. DOI: 10.1115/1.3269198

CHASE D M, NOISEUX C F. Turbulent wall pressure at low wavenumbers: relation to nonlinear sources in planar and cylindrical flow[J]. The Journal of the Acoustical Society of America, 1982, 72(3): 975-982. DOI: 10.1121/1.388179

汤渭霖, 俞孟萨, 王斌. 水动力噪声理论[M]. 北京: 科学出版社, 2019.

KAMRUZZAMAN M, LUTZ T, WÜRZ W, et al. Validations and improvements of airfoil trailing-edge noise prediction models using detailed experimental data[J]. Wind Energy, 2012, 15(1): 45-61. DOI: 10.1002/we.505

BERTAGNOLIO F, FISCHER A, ZHU W J. Tuning of turbulent boundary layer anisotropy for improved surface pressure and trailing-edge noise modeling[J]. Journal of Sound and Vibration, 2014, 333(3): 991-1010. DOI: 10.1016/j.jsv.2013.10.008

COLES D. The law of the wake in the turbulent boundary layer[J]. Journal of Fluid Mechanics, 1956, 1(2): 191-226. DOI: 10.1017/s0022112056000135

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. DOI: 10.1016/0022-460X(77)90391-1

ARGUILLAT B, RICOT D, BAILLY C, et al. Measured wavenumber: frequency spectrum associated with acoustic and aerodynamic wall pressure fluctuations[J]. The Journal of the Acoustical Society of America, 2010, 128(4): 1647-1655. doi: 10.1121/1.3478780

PRIGENT S L, BAILLY C. From shear stress to wall pressure spectra: a semi-analytical approach to account for mean pressure gradients in turbulent boundary layers[J]. Acta Acustica, 2022, 6: 43. DOI: 10.1051/aacus/2022034

KISSNER C A, GUERIN S, BIANCHI S, et al. On the modeling of wall surface pressure spectra for trailing edge noise prediction[C]//28th AIAA/CEAS Aeroacoustics 2022 Conference. Southampton, UK, 2022. doi: 10.2514/6.2022-2800.

FRITSCH D J, VISHWANATHAN V, TODD LOWE K, et al. Fluctuating pressure beneath smooth wall boundary layers in nonequilibrium pressure gradients[J]. AIAA Journal, 2022, 60(8): 4725-4743. DOI: 10.2514/1.j061431

GRASSO G, JAISWAL P, WU H, et al. Analytical models of the wall-pressure spectrum under a turbulent boundary layer with adverse pressure gradient[J]. Journal of Fluid Mechanics, 2019, 877: 1007-1062. DOI: 10.1017/jfm.2019.616