Hostname: page-component-6bf8c574d5-b4m5d Total loading time: 0 Render date: 2025-02-26T22:20:10.190Z Has data issue: false hasContentIssue false
  • English
  • Français

Influence of pressure gradients on wall pressure beneath a turbulent boundary layer

Published online by Cambridge University Press:  22 January 2018

Elie Cohen  and
Xavier Gloerfelt Open the ORCID record for Xavier Gloerfelt [Opens in a new window]
Elie Cohen
Affiliation:
DynFluid Laboratory, Arts et Métiers ParisTech, 151 Boulevard de l’Hôpital, 75013 Paris, France
Xavier Gloerfelt*
Affiliation:
DynFluid Laboratory, Arts et Métiers ParisTech, 151 Boulevard de l’Hôpital, 75013 Paris, France
*
†Email address for correspondence: xavier.gloerfelt@ensam.eu
Get access Rights & Permissions [Opens in a new window]

Abstract

This study investigates the effects of a pressure gradient on the wall pressure beneath equilibrium turbulent boundary layers. Excitation of the walls of a vehicle by turbulent boundary layers indeed constitutes a major source of interior noise and it is necessary to take into account the presence of a pressure gradient to represent the effect of the curvature of the walls. With this aim, large-eddy simulations of turbulent boundary layers in the presence of both mild adverse and mild favourable pressure gradients are carried out by solving the compressible Navier–Stokes equations. This method provides both the aeroacoustic contribution and the hydrodynamic wall-pressure fluctuations. A critical comparison with existing databases, including recent measurements, is conducted to assess the influence of a free stream pressure gradient. The analyses of wall-pressure spectral densities show an increase in the low-frequency content from adverse to favourable conditions, yielding higher integrated levels of pressure fluctuations scaled by the wall shear stress. This is accompanied by a steeper decay rate in the medium-frequency portion for adverse pressure gradients. No significant difference is found for the mean convection velocity. Frequency–wavenumber spectra including the subconvective region are presented for the first time in the presence of a pressure gradient. A scaling law for the convective ridge is proposed, and the acoustic domain is captured by the simulations. Direct acoustic emissions have similar features in all gradient cases, even if slightly higher levels are noted for boundary layers subjected to an adverse gradient.

JFM classification

Acoustics: Aeroacoustics Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 838 , 10 March 2018 , pp. 715 - 758
Check for updates
Copyright
© 2018 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.)

References

Abraham, B. M. & Keith, W. L. 1998 Direct measurements of turbulent boundary-layer wall pressure wavenumber-frequency spectra. Trans. ASME J. Fluids Engng 13, 29–39.CrossRefGoogle 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
Aubard, G., Stefanin Volpiani, P., Gloerfelt, X. & Robinet, J.-C. 2013 Comparison of subgrid-scale viscosity models and selective filtering strategy for large-eddy simulations. Flow Turbul. Combust. 91 (3), 497–518.Google Scholar
Blake, W. K. 1970 Turbulent boundary-layer wall-pressure fluctuations on smooth and rough walls. J. Fluid Mech. 44, 637–660.CrossRefGoogle Scholar
Blake, W. K.1986 Mechanics of Flow-Induced Sound and Vibration, vol. 2: Complex Flow–Structure Interaction, chap. 8, Essentials of turbulent wall pressure fluctuations, pp. 497–594. Academic Press.Google Scholar
Blake, W. K. & Chase, D. M. 1971 Wavenumber-frequency spectra of turbulent-boundary-layer pressure measured by microphone arrays. J. Acoust. Soc. Am. 49 (3), 862–877.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
Bradshaw, P. 1967a ‘Inactive’ motion and pressure fluctuations in turbulent boundary layers. J. Fluid Mech. 30 (2), 241–258.CrossRefGoogle Scholar
Bradshaw, P. 1967b The turbulent structure of equilibrium boundary layers. J. Fluid Mech. 29 (4), 625–645.CrossRefGoogle Scholar
Bull, M. K. 1967 Wall-pressure fluctuations associated with subsonic boundary layer flow. J. Fluid Mech. 28, 719–754.Google Scholar
Bull, M. K. & Thomas, A. S. W. 1976 High-frequency wall-pressure fluctuations in turbulent boundary layers. Phys. Fluids 19 (5), 597–599.Google Scholar
Burton, T. E.1973 Wall pressure fluctuations at smooth and rough surfaces under turbulent boundary layers with favorable and adverse pressure gradients. Report ONR AD 772-548. Massachusetts Institute of Technology.Google Scholar
Capon, J. 1969 High-resolution frequency-wavenumber spectrum analysis. Proc. IEEE 57 (8), 1408–1418.CrossRefGoogle Scholar
Castillo, L. & George, W. K. 2001 Similarity analysis for turbulent boundary layer with pressure gradient: outer flow. AIAA J. 39 (1), 41–47.Google Scholar
Castillo, L. & Wang, X. 2004 Similarity analysis for nonequilibrium turbulent boundary layers. Trans. ASME J. Fluids Engng 126, 827–834.Google Scholar
Catlett, M. R., Anderson, J. M., Forest, J. B. & Stewart, D. O. 2016 Empirical modeling of pressure spectra in adverse pressure gradient turbulent boundary layers. AIAA J. 54 (2), 569–587.Google Scholar
Catlett, M. R., Forest, J. B., Anderson, J. M. & Stewart, D. O.2014 Empirical spectral model of surface pressure fluctuations beneath adverse pressure gradients. In 20th AIAA/CEAS AeroAcoustics Conference, 16–20 June, Atlanta, Georgia. AIAA Paper 2014-2910.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.CrossRefGoogle Scholar
Chauhan, K. A., Monkewitz, P. A. & Nagib, H. M. 2009 Criteria for assessing experiments in zero pressure gradient boundary layers. Fluid Dyn. Res. 41, 021404.Google Scholar
Clauser, F. H. 1954 Turbulent boundary layers in adverse pressure gradients. J. Aeronaut. Sci. 21 (2), 91–108.Google Scholar
Cohen, E.2015 Etude de la pression pariétale et du bruit de couches limites turbulentes avec gradient de pression. PhD thesis, Ecole Nationale Supérieure d’Arts et Métiers, no. ENAM 0044.Google Scholar
Cohen, E. & Gloerfelt, X.2015 Effect of pressure gradients on turbulent boundary layer noise and wall-pressure fluctuations. In 21st AIAA/CEAS AeroAcoustics Conference, 22–26 June, Dallas, Texas. AIAA Paper 2015-3117.Google Scholar
Coles, D. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191–226.Google Scholar
Corcos, G. M. 1964 The structure of the turbulent pressure field in boundary layer flows. J. Fluid Mech. 18, 353–378.CrossRefGoogle Scholar
Craik, A. D. D. 1971 Non-linear resonant instability in boundary layers. J. Fluid Mech. 50 (2), 393–413.CrossRefGoogle Scholar
Curle, N. 1955 The influence of solid boundaries upon aerodynamic sound. Proc. R. Soc. Lond. A 231, 505–514.Google Scholar
Debert, S., Pachebat, M., Valeau, V. & Gervais, Y. 2011 Ensemble-empirical-mode-decomposition method for instantaneous spatial-multi-scale decomposition of wall-pressure fluctuations under a turbulent flow. Exp. Fluids 50, 339–350.CrossRefGoogle 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
Emmerling, R., Meier, G. E. A. & Dinkelacker, A. 1973 Investigation of the instantaneous structure of the wall pressure under a turbulent boundary layer flow. AGARD Conf. Noise Mech. 131, 21–1–24–12.Google Scholar
Erm, L. P. & Joubert, P. N. 1991 Low-Reynolds-number turbulent boundary layers. J. Fluid Mech. 230, 1–44.CrossRefGoogle 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
Forest, J. B.2012 The wall pressure spectrum of high Reynolds number rough-wall turbulent boundary layers. Master’s thesis, Virginia Tech, supervised by W. J. Devenport.Google Scholar
Gloerfelt, X. & Berland, J. 2013 Turbulent boundary-layer noise: direct radiation at Mach number 0.5. J. Fluid Mech. 723, 318–351.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. & Margnat, F.2014 Effect of mach number on boundary layer noise. In 20th AIAA/CEAS AeroAcoustics Conference, 16–20 June, Atlanta, Georgia. AIAA Paper 2014-3291.Google Scholar
Gloerfelt, X. & Robinet, J.-C.2013 A silent inflow condition for the study of boundary layer noise. In 19th AIAA/CEAS AeroAcoustics Conference, 27–29 May, Berlin, Germany. AIAA Paper 2013-2247.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
Harun, Z., Monty, J. P., Mathis, R. & Marusic, I. 2013 Pressure gradient effects on the large-scale structure of turbulent boundary layers. J. Fluid Mech. 715, 477–498.Google Scholar
Herring, H. J. & Norbury, J. F. 1967 Some experiments on equilibrium turbulent boundary layers in favourable pressure gradients. J. Fluid Mech. 27 (3), 541–549.Google Scholar
Hu, N. & Herr, M.2016 Characteristics of wall pressure fluctuations for a flat plate turbulent boundary layer with pressure gradients. In 22nd AIAA/CEAS AeroAcoustics Conference, 30 May–1 June, Lyon, France. AIAA Paper 2016-2749.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. 2006 Wall pressure and shear stress spectra from direct simulations of channel flow. AIAA J. 44, 1541–1549.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.Google Scholar
Jones, M. B., Marusic, I. & Perry, A. E. 2001 Evolution and structure of sink-flow turbulent boundary layers. J. Fluid Mech. 428, 1–27.CrossRefGoogle Scholar
Kader, B. A. & Yaglom, A. M. 1981 Similarity treatment of moving-equilibrium turbulent boundary layers in adverse pressure gradients. J. Fluid Mech. 113, 91–122.Google Scholar
Karangelen, C. C., Wilczynsi, V. & Casarella, M. J. 1993 Large amplitude wall pressure events beneath a turbulent boundary layer. Trans. ASME J. Fluids Engng 115 (3), 653–659.Google Scholar
Kay, S. 1988 Minimum variance spectral estimation. In Modern Spectral Estimation: Theory and Application, chap. 11. Prentice Hall.Google Scholar
Klewicki, J. C., Priyadarshana, P. J. A. & Metzger, M. M. 2008 Statistical structure of the fluctuating wall pressure and its in-plane gradients at high Reynolds number. J. Fluid Mech. 609, 195–220.CrossRefGoogle Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30 (4), 741–773.Google 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
Lewkowicz, A. K. 1982 An improved universal wake function for turbulent boundary layers and some of its consequences. Z. Flugwiss. Weltraumforsch. 6, 261–266.Google Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically. Part I. General theory. Proc. R. Soc. Lond. A 211, 564–587.Google Scholar
Löfdahl, L. & Gad-el Hak, M. 1999 MEMS-based pressure and shear stress sensors for turbulent flows. Meas. Sci. Technol. 10, 665–686.Google Scholar
Löfdahl, L., Kalvesten, E. & Stemme, G. 1996 Small silicon pressure transducers for space–time correlation measurements in a flat plate boundary layer. Trans. ASME J. Fluids Engng 118, 457–463, discussions by P. R. Bandyopadhyay, R. L. Panton, W. L. Keith, T. M. Farabee & M. J. Casarella, and the authors, pp. 879–881.Google Scholar
Maciel, Y., Rossignol, K.-S. & Lemay, J. 2006 Self-similarity in the outer region of adverse-pressure-gradient turbulent boundary layers. AIAA J. 44 (11), 2450–2464.Google Scholar
Marusic, I. & Perry, A. E. 1995 A wall-wake model for the turbulence structure of boundary layers. Part 2. Further experimental support. J. Fluid Mech. 298, 389–407.CrossRefGoogle Scholar
McGrath, B. E. & Simpson, R. L.1987 Some features of surface pressure fluctuations in turbulent boundary layers with zero and favorable pressure gradients. Tech. Rep. CR-4051. NASA.Google Scholar
Mellen, R. H. 1994 Wave-vector filter analysis of turbulent flow. J. Acoust. Soc. Am. 95 (3), 1671–1673.CrossRefGoogle Scholar
Mellor, G. L. 1966 The effects of pressure gradients on turbulent flow near a smooth wall. J. Fluid Mech. 24 (2), 255–274.Google Scholar
Monty, J. P., Harun, Z. & Marusic, I. 2011 A parametric study of adverse pressure gradient turbulent boundary layers. Intl J. Heat Fluid Flow 32, 575–585.Google Scholar
Musker, D. 1979 Explicit expression for the smooth wall velocity distribution in a turbulent boundary layer. AIAA J. 17, 655–657.Google Scholar
Na, Y. & Moin, P. 1998 The structure of wall-pressure fluctuations in turbulent boundary layers with adverse pressure gradient and separation. J. Fluid Mech. 377, 347–373.Google Scholar
Nagano, Y., Tsuji, T. & Houra, T. 1998 Structure of turbulent boundary layer subjected to adverse pressure gradient. Intl J. Heat Fluid Flow 19, 563–572.Google Scholar
Nagib, H. M. & Chauhan, K. A. 2008 Variations of von Kármán coefficient in canonical flows. Phys. Fluids 20, 101518.CrossRefGoogle Scholar
Panton, R. L. & Linebarger, J. H. 1974 Wall pressure spectra calculations for equilibrium boundary layers. J. Fluid Mech. 65, 261–287.Google Scholar
Panton, R. L. & Robert, G. 1994 The wavenumber-phase velocity representation for the turbulent wall-pressure spectrum. Trans. ASME J. Fluids Engng 116, 477–483.Google Scholar
Powell, A. 1960 Aerodynamic noise and the plane boundary. J. Acoust. Soc. Am. 32 (8), 982–990.CrossRefGoogle Scholar
Rotta, J. 1962 Turbulent boundary layers in incompressible flows. Prog. Aerosp. Sci. 2 (1–2), 1–219.Google Scholar
Salze, E., Bailly, C., Marsden, O., Jondeau, E. & Juvé, D.2014 An experimental characterization of wall pressure wavevector-frequency spectra in the presence of pressure gradients. In 20th AIAA/CEAS AeroAcoustics Conference, 16–20 June, Atlanta, Georgia. AIAA Paper 2014-2909.Google Scholar
Salze, E., Bailly, C., Marsden, O., Jondeau, E. & Juvé, D.2015 An experimental investigation of wall pressure fluctuations beneath pressure gradients. In 21st AIAA/CEAS AeroAcoustics Conference, 22–26 June, Dallas, Texas. AIAA Paper 2015-3148.Google Scholar
Samuel, A. E. & Joubert, P. N. 1974 A boundary layer developing in an increasingly adverse pressure gradient. J. Fluid Mech. 66 (3), 481–505.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.Google Scholar
Schlatter, P. & Örlü, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116–126.Google Scholar
Schloemer, H. H. 1967 Effects of pressure gradients on turbulent-boundary-layer wall-pressure fluctuations. J. Acoust. Soc. Am. 42 (1), 93–113.Google Scholar
Schofield, W. H. 1981 Equilibrium boundary layers in moderate to strong adverse pressure gradients. J. Fluid Mech. 113, 91–122.CrossRefGoogle Scholar
Simpson, R. L., Ghodbane, M. & McGrath, B. E. 1987 Surface pressure fluctuation in a separating turbulent boudary layer. J. Fluid Mech. 177, 167–186.Google Scholar
Skare, P. E. & Krogstad, P.-A. 1994 A turbulent equilibrium boundary layer near separation. J. Fluid Mech. 272, 319–348.Google Scholar
Skote, M., Henningson, D. S. & Henkes, R. A. W. M. 1998 Direct numerical simulation of self-similar turbulent boundary layers in adverse pressure gradients. Flow Turbul. Combust. 60, 47–85.CrossRefGoogle Scholar
Smol’yakov, A. V. 2006 A new model for the cross spectrum and wavenumber-frequency spectrum of turbulent pressure fluctuations in a boundary layer. Acoust. Phys. 52 (3), 331–337.Google Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to Re 𝜃 = 1410. J. Fluid Mech. 187, 61–98.Google Scholar
Spalart, P. R. & Watmuff, J. H. 1993 Experimental and numerical study of a turbulent boundary layer with pressure gradients. J. Fluid Mech. 249, 337–371.CrossRefGoogle Scholar
Strawderman, W. A.1987 Wavevector-frequency spectra of nonhomogeneous fields. NUSC Tech. Docum. 7873. Naval Underwater Systems Center, Newport, Rhode Island/New London, Connecticut, USA, paper presented at the 112th Meeting of the Acoustical Society of America 8–12 December 1986, Anaheim, USA.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
Tani, I. 1986 Some equilibrium turbulent boundary layers. Fluid Dyn. Res. 1, 49–58.Google Scholar
Townsend, A. A. 1961 Equilibrium layers and wall turbulence. J. Fluid Mech. 11 (1), 97–120.Google Scholar
Tsuji, Y., Imayama, S., Schlatter, P., Alfredsson, P. H., Johansson, A. V., Marusic, I., Hutchins, N. & Monty, J. 2012 Pressure fluctuation in high-Reynolds-number turbulent boudary layer: results from experiments and DNS. J. Turbul. 13 (50), 1–19.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
Watmuff, J. H. 1988 An experimental investigation of a low Reynolds number turbulent boundary layer subject to an adverse pressure gradient. In Center for Turbulence Research – Annual Research Briefs, pp. 153–166. Center for Turbulence Research, Stanford University.Google Scholar
White, R. D., Krause, J. S., De Jong, R., Holup, G., Gallman, J. & Moeller, M.2012 MEMS microphone array on a chip for turbulent boundary layer measurements. In 50th AIAA Aerospace Sciences Meeting, 9–12 January, Nashville, USA. AIAA Paper 2012-0260.Google Scholar
Willmarth, W. W. 1975 Pressure fluctuations beneath turbulent boundary layers. Annu. Rev. Fluid Mech. 7, 13–38.Google Scholar
Wills, J. A. B. 1970 Measurements of the wave-number/phase velocity spectrum of wall pressure beneath a turbulent boundary layer. J. Fluid Mech. 45, 65–90.Google Scholar
Witting, J. M. 1986 A spectral model of pressure fluctuations at a rigid wall bounding an incompressible fluid, based on turbulent structures in the boundary layer. Noise Control Engng J. 26 (1), 29–39.Google Scholar
Wosnik, M. & George, W. K.2000 Reconciling the Zaragola–Smits scaling with the George/Castillo theory for the zero pressure gradient turbulent boundary layer. In 38th AIAA Aerospace Sciences Meeting and Exhibit, 10–13 January, Reno, Nevada. AIAA Paper 2000-0911.Google Scholar
Zaragola, M. V. & Smits, A. J. 1997 Scaling of the mean velocity profile for turbulent pipe flow. Phys. Rev. Lett. 78 (2), 239–242.Google Scholar