Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-14T22:46:57.393Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent boundary-layer noise: direct radiation at Mach number 0.5

Published online by Cambridge University Press:  16 April 2013

Xavier Gloerfelt  and
Julien Berland
Xavier Gloerfelt*
Affiliation:
DynFluid Laboratory, Arts et Metiers ParisTech, 151 boulevard de l’Hopital, 75013 Paris, France
Julien Berland
Affiliation:
DynFluid Laboratory, Arts et Metiers ParisTech, 151 boulevard de l’Hopital, 75013 Paris, France
*
†Email address for correspondence: xavier.gloerfelt@paris.ensam.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

Boundary layers constitute a fundamental source of aerodynamic noise. A turbulent boundary layer over a plane wall can provide an indirect contribution to the noise by exciting the structure and a direct noise contribution. The latter part can play a significant role even if its intensity is very low, explaining why it is difficult to measure. In the present study, the aerodynamic noise generated by a spatially developing turbulent boundary layer is computed directly by solving the compressible Navier–Stokes equations. This numerical experiment aims at giving some insight into the noise radiation characteristics. The acoustic wavefronts have a large wavelength and are oriented in the direction opposite to the flow. Their amplitude is only 0.7 % of the aerodynamic pressure for a flat-plate flow at Mach 0.5. The particular directivity is mainly explained by convection effects by the mean flow, giving an indication about the compactness of the sources. These vortical events correspond to low frequencies and thus have a large lifetime. They cannot be directly associated with the main structures populating the boundary layer such as hairpin or horseshoe vortices. The analysis of the wall pressure can provide a picture of the flow in the wavenumber–frequency space. The main features of wall pressure beneath a turbulent boundary layer as described in the literature are well reproduced. The acoustic domain, corresponding to supersonic wavenumbers, is detectable but can hardly be separated from the convective ridge at this relatively high speed. This is also due to the low frequencies of sound emission as noted previously.

JFM classification

Acoustics: Aeroacoustics Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 723 , 25 May 2013 , pp. 318 - 351
Copyright
©2013 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

‡

Present address: EDF R&D, MFEE, I84, 6 Quai Watier, 78400 Chatou, France.

References

Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.Google Scholar
Arguillat, B. 2006 Etude expérimentale et numérique de champs de pression pariétale dans l’espace des nombres d’onde, avec application aux vitrages automobiles. PhD thesis, Ecole Centrale de Lyon, no 2006-14.Google Scholar
Arguillat, B., Ricot, D., Robert, G. & Bailly, C. 2010 Measured wavenumber–frequency spectrum associated with acoustic and aerodynamic wall pressure fluctuations. J. Acoust. Soc. Am. 128 (4), 1647–1655.CrossRefGoogle ScholarPubMed
Barker, S. J. 1973 Radiated noise from turbulent boundary layers in dilute polymer solutions. Phys. Fluids 16, 1387–1394.Google Scholar
Beresh, S. J., Henfling, J. F., Spillers, R. W. & Pruett, B. O. M. 2011 Fluctuating wall pressures measured beneath a supersonic turbulent boundary layer. Phys. Fluids 23, 075110.Google Scholar
Bergeron, R. F. 1974 Acoustic sources in the low Mach number turbulent boundary layer. J. Acoust. Soc. Am. 54 (1), 123–133.Google Scholar
Berland, J. & Gloerfelt, X. 2008 Investigation of noise radiation from a turbulent boundary layer. In 14th AIAA/CEAS AeroAcoustics Conference, 5–7 May, Vancouver, Canada, AIAA Paper 2008-2802.Google Scholar
Blake, W. K. 1970 Turbulent boundary-layer wall-pressure fluctuations on smooth and rough walls. J. Fluid Mech. 44, 637–660.Google Scholar
Blake, W. K. 1986a Essentials of turbulent wall-pressure fluctuations. In Mechanics of Flow-induced Sound and Vibration, vol. 2: Complex Flow-structure Interaction , pp. 497–594. Academic Press.Google Scholar
Blake, W. K. 1986b Mechanics of Flow-induced Sound and Vibration, vol. 2 Complex Flow-structure Interaction . Structural Response to Turbulent Wall Flow and Random Sound, chap. 9, pp. 595–657. Academic Press.Google Scholar
Bogey, C. & Bailly, C. 2002 Three-dimensional non-reflective boundary conditions for acoustic simulations: far field formulation and validation test cases. Acta Acust. 88, 463–471.Google Scholar
Bogey, C. & Bailly, C. 2004 A family of low dispersive and low dissipative explicit schemes for noise computation. J. Comput. Phys. 194, 194–214.Google Scholar
Bogey, C. & Bailly, C. 2006 Large eddy simulations of round jets using explicit filtering with/without dynamic Smagorinsky model. Intl J. Heat Fluid Flow 27, 603–610.Google Scholar
Bull, M. K. 1967 Wall-pressure fluctuations associated with subsonic boundary layer flow. J. Fluid Mech. 28, 719–754.CrossRefGoogle Scholar
Bull, M. K. 1996 Wall-pressure fluctuations beneath turbulent boundary layers: some reflections on forty years of research. J. Sound Vib. 190 (3), 299–315.Google Scholar
Chang, P., Piomelli, U. & Blake, W. 1999 Relationship between wall pressure and velocity sources. Phys. Fluids 11 (11), 3434–3448.CrossRefGoogle Scholar
Chase, D. M. 1980 Modeling the wavevector–frequency spectrum of turbulent boundary layer wall pressure. J. Sound Vib. 70, 29–67.Google Scholar
Chase, D. M. 1987 The character of the turbulent wall pressure spectrum at subconvective wavenumbers and a suggested comprehensive model. J. Sound Vib. 112 (1), 125–147.Google Scholar
Choi, H. & Moin, P. 1990 On the space–time characteristics fo wall-pressure fluctuations. Phys. Fluids A 2 (8), 1450–1460.CrossRefGoogle Scholar
Corcos, G. M. 1963 Resolution of pressure in turbulence. J. Acoust. Soc. Am. 35, 192–199.Google Scholar
Curle, N. 1955 The influence of solid boundaries upon aerodynamic sound. Proc. R. Soc. Lond. A 231, 505–514.Google Scholar
Dowling, A. P. 1992 Flow noise on surfaces. In Modern Methods in Analytical Acoustics: Lectures Notes (ed. Crighton, D. G., Dowling, A. P., Ffowcs Williams, J. E., Heckl, M. & Leppington, F. G.), pp. 452–509. Springer.Google Scholar
Ehrenfried, K. & Koop, L. 2008. Experimental study of pressure fluctuations beneath a compressible turbulent boundary layer. In 14th AIAA/CEAS AeroAcoustics Conference, 5–7 May, Vancouver, Canada, AIAA Paper 2008-2800.Google Scholar
Farabee, T. M. & Casarella, M. J. 1991 Spectral features of wall pressure fluctuations beneath turbulent boundary layers. Phys. Fluids A 3 (10), 2410–2420.Google Scholar
Ffowcs Williams, J. E. 1965 Surface-pressure fluctuations induced by boundary-layer flow at finite Mach number. J. Fluid Mech. 22, 507–519.Google Scholar
Ffowcs Williams, J. E. 1982 Boundary-layer pressures and the Corcos model: a development to incorporate low-wavenumber constraints. J. Fluid Mech. 125, 9–25.Google Scholar
Garnier, E., Adams, N. & Sagaut, P. 2009 Large Eddy Simulation for Compressible Flows. Springer.Google Scholar
Gloerfelt, X. 2010. The link between wall pressure spectra and radiated sound from turbulent boundary layers. 16th AIAA/CEAS AeroAcoustics Conference, 7–9 June, Stockholm, Sweeden, AIAA Paper 2010-3904.Google Scholar
Gloerfelt, X. & Berland, J. 2009 Direct computation of turbulent boundary layer noise. In 15th AIAA/CEAS AeroAcoustics Conference, 11–13 May, Miami, FL, AIAA Paper 2009-3401.Google Scholar
Gloerfelt, X. & Lafon, P. 2008 Direct computation of the noise induced by a turbulent flow through a diaphragm in a duct at low Mach number. Comput. Fluids 37, 388–401.Google Scholar
Gloerfelt, X. & Le Garrec, T. 2008 Generation of inflow turbulence for aeroacoustic applications. In 14th AIAA/CEAS AeroAcoustics Conference, 5–7 May, Vancouver, Canada, AIAA Paper 2008-2926.Google Scholar
Goody, M. 2004 Empirical spectral model of surface pressure fluctuations. AIAA J. 42 (9), 1788–1794.Google Scholar
Graham, W. R. 1997 A comparison of models for the wavenumber–frequency spectrum of turbulent boundary layer pressures. J. Sound Vib. 206 (4), 541–565.Google Scholar
Gravante, S. P., Naguib, A. M., Wark, C. E. & Nagib, H. M. 1998 Characterization of the pressure fluctuations under a fully developed turbulent boundary layer. AIAA J. 36 (10), 1808–1816.Google Scholar
Greshilov, E. M. & Mironov, M. A. 1983 Experimental evaluation of sound generated by turbulent flow in a hydrodynamic duct. Sov. Phys. Acoust. 29, 275–280.Google Scholar
Gustafsson, F. 1996 Determining the initial states in forward–backward filtering. IEEE Trans. Signal Process. 44 (4), 988–992.CrossRefGoogle Scholar
Haddle, G. P. & Skudrzyk, E. J. 1969 The physics of flow noise. J. Acoust. Soc. Am. 46 (1), 130–157.Google Scholar
Haj-Hariri, H. & Akylas, T. R. 1985 The wall-shear-stress contribution to boundary-layer noise. Phys. Fluids 28 (9), 2727–2729.CrossRefGoogle Scholar
Hardin, J. C. 1991 Acoustic sources in the low Mach number turbulent boundary layer. J. Acoust. Soc. Am. 90 (2), 1020–1031.Google Scholar
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary layer structures. J. Fluid Mech. 107, 297–338.Google Scholar
Howe, M. S. 1979a The interaction of sound with low Mach number wall turbulence, with application to sound propagation in turbulent pipe flow. J. Fluid Mech. 94 (4), 729–744.Google Scholar
Howe, M. S. 1979b The rôle of surface shear stress fluctuations in the generation of boundary layer noise. J. Sound Vib. 65 (2), 159–164.Google Scholar
Howe, M. S. 1991 Surface pressures and sound produced by turbulent flow over smooth and rough walls. J. Acoust. Soc. Am. 90 (2), 1041–1047.CrossRefGoogle Scholar
Howe, M. S. 1992 A note on the Kraichnan–Phillips theorem. J. Fluid Mech. 234, 443–448.Google Scholar
Howe, M. S. 1998 Acoustics of Fluid–Structures Interactions. Cambridge University Press.Google Scholar
Hu, Z. W., Morfey, C. L. & Sandham, N. D. 2002 Aeroacoustics of wall-bounded turbulent flows. AIAA J. 40, 465–473.Google Scholar
Hu, Z. W., Morfey, C. L. & Sandham, N. D. 2003 Sound radiation in turbulent channel flows. J. Fluid Mech. 475, 269–302.Google Scholar
Hu, Z. W., Morfey, C. L. & Sandham, N. D. 2006a Sound radiation from a turbulent boundary layer. Phys. Fluids 18, 098101.Google Scholar
Hu, Z. W., Morfey, C. L. & Sandham, N. D. 2006b Wall pressure and shear stress spectra from direct simulations of channel flow. AIAA J. 44, 1541–1549.Google Scholar
Hutchins, N., Monty, J. P., Ganapathisubramani, B., Ng, H. C. & Marusic, I. 2011 Three-dimensional conditional structure of a high-Reynolds-number turbulent boundary layer. J. Fluid Mech. 673, 255–285.Google Scholar
Hwang, Y. F., Bonness, W. K. & Hambric, S. A. 2009 Comparison of semi-empirical models for turbulent boundary layer wall pressure spectra. J. Sound Vib. 319 (1–2), 199–217.Google Scholar
Jimenez, J., Hoyas, S., Simens, M. P. & Mizuno, Y. 2010 Turbulent boundary layers and channels at moderate Reynolds numbers. J. Fluid Mech. 657, 335–360.CrossRefGoogle Scholar
Kim, J. 1989 On the structure of pressure fluctuations in simulated turbulent channel flow. J. Fluid Mech. 205, 421–451.Google Scholar
Kraichnan, R. H. 1956 Pressure fluctuations in a turbulent flow over a flat plate. J. Acoust. Soc. Am. 28 (3), 378–390.CrossRefGoogle Scholar
Landahl, M. T. 1975 Wave mechanics of boundary layer turbulence and noise. J. Acoust. Soc. Am. 57 (4), 824–831.Google Scholar
Lauchle, G. C. 1980 On the radiated noise due to boundary layer transition. J. Acoust. Soc. Am. 67 (1), 158–168.CrossRefGoogle Scholar
Leclercq, D. J. J. & Bohineust, X. 2002 Investigation and modelling of the wall pressure field beneath a turbulent boundary layer at low and medium frequencies. J. Sound Vib. 257 (3), 477–501.Google Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically I. General theory. Proc. R. Soc. Lond. A 211, 564–587.Google Scholar
Lund, T. S., Wu, X. & Squires, K. D. 1998 Generation of turbulent inflow data for spatially-developing boundary layer simulations. J. Comput. Phys. 140, 233–258.Google Scholar
Mathew, J., Lechner, R., Foysi, H., Sesterhenn, J. & Friedrich, R. 2003 An explicit filtering method for large eddy simulation of compressible flows. Phys. Fluids 15 (8), 2279–2289.Google Scholar
Meecham, W. C. 1965 Surface and volume sound from boundary layers. J. Acoust. Soc. Am. 37, 516–522.Google Scholar
Panton, R. L. & Robert, G. 1994 The wavenumber-phase velocity representation for the turbulent wall-pressure spectrum. Trans. ASME: ASME J. Fluids Engng 116, 477–483.Google Scholar
Phillips, O. M. 1956 On the aerodynamic surface sound from a plane turbulent boundary layer. Proc. R. Soc. Lond. 234, 327–335.Google Scholar
Powell, A. 1960 Aerodynamic noise and the plane boundary. J. Acoust. Soc. Am. 32 (8), 982–990.Google Scholar
Robinet, J.-C., Dussauge, J.-P. & Casalis, G. 2001 Wall effect on the convective-absolute boundary for the compressible shear layer. Theor. Comput. Fluid Dyn. 15, 143–163.Google Scholar
Schewe, G. 1983 On the structure and resolution of wall-pressure fluctuations associated with turbulent boundary-layer flow. J. Fluid Mech. 134, 311–328.CrossRefGoogle Scholar
Sevik, M. M. 1986 Topic in hydroacoustics. In IUTAM Symp. on Aero- and Hydro-acoustics, pp. 285–308. Springer.Google Scholar
Shariff, K. & Wang, M. 2005 A numerical experiment to determine whether surface shear-stress fluctuations are true sound source. Phys. Fluids 17 (107105).CrossRefGoogle Scholar
Skudrzyk, F. J. & Haddle, G. P. 1960 Noise production in a turbulent boundary layer by smooth and rough surfaces. J. Acoust. Soc. Am. 32 (1), 19–34.CrossRefGoogle Scholar
Smith, M. G. & Morfey, C. L. 2006 Directivity and sound power radiated by a source under a boundary layer. AIAA J. 44 (11), 2630–2635.Google Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to ${\mathit{Re}}_{\theta } = 1410$ . J. Fluid Mech. 187, 61–98.Google Scholar
Suzuki, T. & Lele, S. K. 2003 Green’s functions for a source in a boundary layer: direct waves, channelled waves and diffracted waves. J. Fluid Mech. 447, 129–173.Google Scholar
Tam, C. K. W. 1975 Intensity, spectrum, and directivity of turbulent boundary layer noise. J. Acoust. Soc. Am. 57 (1), 25–34.Google Scholar
Tam, C. K. W. & Dong, Z. 1996 Radiation and outflow boundary conditions for direct computation of acoustic and flow disturbances in a nonuniform mean flow. J. Comput. Acoust. 4 (2), 175–201.Google Scholar
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 37–74.Google Scholar
Viazzo, S., Dejoan, A. & Schiestel, R. 2001 Spectral features of the wall-pressure fluctuations in turbulent wall flows with and without perturbations using LES. Intl J. Heat Fluid Flow 22, 39–52.Google Scholar
Wang, M., Lele, S. K. & Moin, P. 1996 Sound radiation during local laminar berakdown in a low-Mach-number boundary layer. J. Fluid Mech. 319, 197–218.Google Scholar
Willmarth, W. W. 1975 Pressure fluctuations beneath turbulent boundary layers. Annu. Rev. Fluid Mech. 7, 13–38.Google Scholar
Willmarth, W. W. & Woolridge, C. E. 1962 Measurements of the fluctuating pressure at the wall beneath a thick turbulent boundary layer. J. Fluid Mech. 14, 187–210.Google Scholar
Wills, J. A. B. 1970 Measurements of the wavenumber/phase velocity spectrum of wall pressure beneath a turbulent boundary layer. J. Fluid Mech. 45, 65–90.Google Scholar
Yang, Q. & Wang, M. 2009 Computational study of roughness-induced boundary-layer noise. AIAA J. 47 (10), 2417–2429.Google Scholar

Gloerfelt and Berland supplementary movie

Colormap of the pressure fluctuations p' in the median plane (range ±5 Pa) for the fine-grid LES. Broadband noise is radiated from the turbulent boundary layer (TBL) with wavefronts oriented in the upstream direction. Important time-to-time variations are visible for the large-wavelength pressure lobes advected in the TBL.

Download Gloerfelt and Berland supplementary movie(Video)
Video 10.6 MB

Gloerfelt and Berland supplementary movie

Band-pass filtered pressure around ωU∞/δ*ref=0.033, corresponding to the peak value of the low-frequency bump. 2-D view in the median plane (range ±0.7 Pa). Near the wall, large lobes corresponding to aerodynamic pressure are advected, and the acoustic waves are clearly connected with their evolution.

Download Gloerfelt and Berland supplementary movie(Video)
Video 5.5 MB

Gloerfelt and Berland supplementary movie

Band-pass filtered pressure around ωU∞/δ*ref=0.20, corresponding to the end of the low-frequency bump. 2-D view in the median plane (range ±0.2 Pa). For this smaller wavelength, it is possible to identify approximately the location and duration of well-defined compact sources. The animation shows that these sources are not advected with the boundary layer, but are rather at fixed locations, and have a large life time. The structure and "breathing" behaviour of the near-field pressure lobes can also be observed.

Download Gloerfelt and Berland supplementary movie(Video)
Video 5.5 MB

Gloerfelt and Berland supplementary movie

Band-pass filtered pressure in the frequency band ωU∞/δ*ref∈[0.52;0.99], corresponding to the bounds of the first high-frequency peak. 2-D view in the median plane (range ±2 Pa). The radiation levels are significantly higher in the inlet region, where a small step is used to ignite the eruption of turbulence. Note also that the downstream-oriented part of the wavefronts is visible for these high frequencies, yielding a complex interference pattern.

Download Gloerfelt and Berland supplementary movie(Video)
Video 5.5 MB