Shock Waves

, Volume 29, Issue 1, pp 117–134 | Cite as

Identification of temporal and spatial signatures of broadband shock-associated noise

  • C. Pérez Arroyo
  • G. DavillerEmail author
  • G. Puigt
  • C. Airiau
  • S. Moreau
Original Article


Broadband shock-associated noise (BBSAN) is a particular high-frequency noise that is generated in imperfectly expanded jets. BBSAN results from the interaction of turbulent structures and the series of expansion and compression waves which appears downstream of the convergent nozzle exit of moderately under-expanded jets. This paper focuses on the impact of the pressure waves generated by BBSAN from a large eddy simulation of a non-screeching supersonic round jet in the near-field. The flow is under-expanded and is characterized by a high Reynolds number \(\mathrm{Re}_\mathrm{j} = 1.25\times 10^6\) and a transonic Mach number \(M_\mathrm{j}=1.15\). It is shown that BBSAN propagates upstream outside the jet and enters the supersonic region leaving a characteristic pattern in the physical plane. This pattern, also called signature, travels upstream through the shock-cell system with a group velocity between the acoustic speed \(U_{\mathrm{c}}-a_\infty \) and the sound speed \(a_\infty \) in the frequency–wavenumber domain \((U_\mathrm{c}\) is the convective jet velocity). To investigate these characteristic patterns, the pressure signals in the jet and the near-field are decomposed into waves traveling downstream (\(p^+\)) and waves traveling upstream (\(p^-\)). A novel study based on a wavelet technique is finally applied on such signals in order to extract the BBSAN signatures generated by the most energetic events of the supersonic jet.


LES Identification Shock cells Jet noise Wavelet analysis 



The authors are thankful to L. Gefen from Università Degli Study di Roma, UniRomaTre for his help with the wavelet post-processing. This work was granted access to the HPC resources of CINES under the allocation 2016-[x20162a6074] made by GENCI. Moreover, It was supported by the Marie Curie Initial Training Networks (ITN) AeroTraNet 2 of the European Community’s Seventh Framework Programme (FP7) under Contract No. PITN-GA-2012-317142.


  1. 1.
    Powell, A.: On the mechanism of choked jet noise. Proc. Phys. Soc. Lond. Sect. B 66(12), 1039 (1953). CrossRefGoogle Scholar
  2. 2.
    Harper-Bourne, M., Fisher, M.J.: The noise from shock waves in supersonic jets. In: Advisory Group for Aerospace Research and Development. AGARD-CP-131 (1973)Google Scholar
  3. 3.
    Tam, C.K.W., Tanna, H.K.: Shock associated noise of supersonic jets from convergent–divergent nozzles. J. Sound Vib. 81(3), 337–358 (1982). CrossRefzbMATHGoogle Scholar
  4. 4.
    Norum, T.D., Seiner, J.M.: Broadband shock noise from supersonic jets. AIAA J. 20(1), 68–73 (1982). CrossRefGoogle Scholar
  5. 5.
    Krothapalli, A., Hsia, Y., Baganoff, D., Karamcheti, K.: The role of screech tones in mixing of an underexpanded rectangular jet. J. Sound Vib. 106(1), 119–143 (1986). CrossRefGoogle Scholar
  6. 6.
    Tam, C.K.W.: Stochastic model theory of broadband shock associated noise from supersonic jets. J. Sound Vib. 116(2), 265–302 (1987). CrossRefGoogle Scholar
  7. 7.
    Tam, C.K.W., Golebiowski, M., Seiner, J.M.: On the two components of turbulent mixing noise from supersonic jets. In: 2nd AIAA/CEAS Aeroacoustics Conference, 6–8 May, State College, Pennsylvania, AIAA Paper 1996-1716 (1996).
  8. 8.
    Raman, G.: Supersonic jet screech: half-century from Powell to the present. J. Sound Vib. 225(3), 543–571 (1999). CrossRefGoogle Scholar
  9. 9.
    Tam, C.K.W.: Supersonic jet noise. Annu. Rev. Fluid Mech. 27(1), 17–43 (1995). CrossRefGoogle Scholar
  10. 10.
    Manning, T.A., Lele, S.K.: A numerical investigation of sound generation in supersonic jet screech. DTIC document, Standford University (1999)Google Scholar
  11. 11.
    Suzuki, T., Lele, S.K.: Shock leakage through an unsteady vortex-laden mixing layer: application to jet screech. J. Fluid Mech. 490, 139–167 (2003). CrossRefzbMATHGoogle Scholar
  12. 12.
    Berland, J., Bogey, C., Bailly, C.: Large eddy simulation of screech tone generation in a planar underexpanded jet. In: 12th AIAA/CEAS Aeroacoustics Conference (27th AIAA Aeroacoustics Conference), 8–10 May, Cambridge, Massachusetts, AIAA Paper 2006-2496 (2006).
  13. 13.
    Schulze, J., Sesterhenn, J.: Numerical simulation of supersonic jet-noise. Proc. Appl. Math. Mech. 8(1), 10703–10704 (2008). CrossRefzbMATHGoogle Scholar
  14. 14.
    Schulze, J., Sesterhenn, J., Schmid, P., Bogey, C., de Cacqueray, N., Berland, J., Bailly, C.: Numerical simulation of supersonic jet noise. In: Brun, C., Juvé, D., Manhart, M., Munz, C.-D. (eds.) Numerical Simulation of Turbulent Flows and Noise Generation, pp. 29–46. Springer, Berlin (2009).
  15. 15.
    Mendez, S., Shoeybi, M., Sharma, A., Ham, F.E., Lele, S.K., Moin, P.: Large-eddy simulations of perfectly-expanded supersonic jets: quality assessment and validation. In: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 4–7 January 2010, Orlando, Florida, AIAA Paper 2010-271 (2010).
  16. 16.
    Bodony, D.J., Ryu, J., Lele, S.K.: Investigating broadband shock-associated noise of axisymmetric jets using large-eddy simulation. In: 12th AIAA/CEAS Aeroacoustics Conference, 8–10 May, Cambridge, Massachusetts, AIAA Paper 2006-2495 (2006).
  17. 17.
    Lo, S.C., Aikens, K., Blaisdell, G., Lyrintzis, A.: Numerical investigation of 3-D supersonic jet flows using large-eddy simulation. Int. J. Aeroacoust. 11(7–8), 783–812 (2012). CrossRefGoogle Scholar
  18. 18.
    Nichols, J.W., Ham, F.E., Lele, S.K., Moin, P.: Prediction of supersonic jet noise from complex nozzles. In: Annual Research Briefs 2011, pp. 3–14. Center for Turbulence Research (2011)Google Scholar
  19. 19.
    Nichols, J., Ham, F., Lele, S., Bridges, J.: Aeroacoustics of a supersonic rectangular jet: experiments and LES predictions. In: 50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 9–12 January, Nashville, Tennessee, AIAA Paper 2012-0678 (2012).
  20. 20.
    Brès, G.A., Ham, F.E., Nichols, J.W., Lele, S.K.: Unstructured large-eddy simulations of supersonic jets. AIAA J. 55(4), 1164–1184 (2017). CrossRefGoogle Scholar
  21. 21.
    Morlet, J.: Sampling theory and wave-propagation. In: Chen, C.H. (ed.) Issues in Acoustic Signal–Image Processing and Recognition, pp. 233–261. Springer, Berlin (1983). CrossRefGoogle Scholar
  22. 22.
    Farge, M.: Wavelet transforms and their applications to turbulence. Annu. Rev. Fluid Mech. 24(1), 395–458 (1992). MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Camussi, R., Guj, G.: Orthonormal wavelet decomposition of turbulent flows: intermittency and coherent structures. J. Fluid Mech. 348, 177–199 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Camussi, R., Guj, G.: Experimental analysis of intermittent coherent structures in the near field of a high Re turbulent jet flow. Phys. Fluids 11(2), 423–431 (1999). CrossRefzbMATHGoogle Scholar
  25. 25.
    Grassucci, D., Camussi, R., Jordan, P., Grizzi, S.: Intermittency of the near pressure field induced by a compressible coaxial jet. Exp. Fluids 56(2), 1–13 (2015). CrossRefGoogle Scholar
  26. 26.
    Camussi, R., Grilliat, J., Caputi-Gennaro, G., Jacob, M.C.: Experimental study of a tip leakage flow: wavelet analysis of pressure fluctuations. J. Fluid Mech. 660, 87–113 (2010). CrossRefzbMATHGoogle Scholar
  27. 27.
    Grizzi, S., Camussi, R.: Wavelet analysis of near-field pressure fluctuations generated by a subsonic jet. J. Fluid Mech. 698, 93–124 (2012). CrossRefzbMATHGoogle Scholar
  28. 28.
    Crawley, M., Samimy, M.: Decomposition of the near-field pressure in an excited subsonic jet. In: 20th AIAA/CEAS Aeroacoustics Conference, 16–20 June, Atlanta, Georgia, AIAA Paper 2014-2342 (2014).
  29. 29.
    Mancinelli, M., Pagliaroli, T., Di Marco, A., Camussi, R., Castelain, T.: Wavelet decomposition of hydrodynamic and acoustic pressures in the near field of the jet. J. Fluid Mech. 813, 716–749 (2017). MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Cavalieri, A., Daviller, G., Comte, P., Jordan, P., Tadmor, G., Gervais, Y.: Using large eddy simulation to explore sound-source mechanisms in jets. J. Sound Vib. 330(17), 4098–4113 (2011). CrossRefGoogle Scholar
  31. 31.
    Walker, S.H., Gordeyev, S.V., Thomas, F.O.: A wavelet transform analysis applied to unsteady aspects of supersonic jet screech resonance. Exp. Fluids 22(3), 229–238 (1997). CrossRefGoogle Scholar
  32. 32.
    Gefen, L., Pérez Arroyo, C., Camussi, R., Puigt, G., Airiau, C.: Broadband shock-cell noise signature identification using a wavelet-based method. In: 22nd AIAA/CEAS Aeroacoustics Conference, 30 May–1 June, Lyon, AIAA Paper 2016-2732 (2016).
  33. 33.
    Torrence, C., Compo, G.P.: A practical guide to wavelet analysis. Bull. Am. Meteorol. Soc. 79(1), 61–78 (1998).;2 CrossRefGoogle Scholar
  34. 34.
    André, B., Castelain, T., Bailly, C.: Broadband shock-associated noise in screeching and non-screeching underexpanded supersonic jets. AIAA J. 51(3), 665–673 (2013). CrossRefGoogle Scholar
  35. 35.
    Cambier, L., Heib, S., Plot, S.: The Onera \(elsA\) CFD software: input from research and feedback from industry. Mech. Ind. 14(03), 159–174 (2013). CrossRefGoogle Scholar
  36. 36.
    Lele, S.K.: Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42 (1992). MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Fosso-Pouangué, A., Deniau, H., Sicot, F., Sagaut, P.: Curvilinear finite volume schemes using high order compact interpolation. J. Comput. Phys. 229(13), 5090–5122 (2010). MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Visbal, M.R., Gaitonde, D.V.: On the use of higher-order finite-difference schemes on curvilinear and deforming meshes. J. Comput. Phys. 181, 155–185 (2002). MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Bogey, C., Bailly, C.: A family of low dispersive and low dissipative explicit schemes for flow and noise computations. J. Comput. Phys. 194(1), 194–214 (2004). CrossRefzbMATHGoogle Scholar
  40. 40.
    Spalart, P.R., Allmaras, S.: A one-equation turbulence model for aerodynamic flows. In: 30th Aerospace Sciences Meeting and Exhibit, 6–9 January, Reno, Nevada, AIAA Paper 1992-0439 (1992).
  41. 41.
    Shur, M.L., Spalart, P.R., Strelets, M.K.: Noise prediction for increasingly complex jets. Part I: Methods and tests. Int. J. Aeroacoust. 4(3&4), 213–246 (2005).
  42. 42.
    Shur, M.L., Spalart, P.R., Strelets, M.K., Garbaruk, A.V.: Further steps in LES-based noise prediction for complex jets. In: 44th AIAA Aerospace Sciences Meeting and Exhibit, 9–12 January, Reno, Nevada, AIAA Paper 2006-485 (2006).
  43. 43.
    Tam, C.K.W., Dong, Z.: Radiation and outflow boundary conditions for direct computation of acoustic and flow disturbances in a nonuniform mean flow. J. Comput. Phys. 4(02), 175–201 (1996). Google Scholar
  44. 44.
    Bogey, C., Bailly, C.: Three-dimensional non-reflective boundary conditions for acoustic simulations: far field formulation and validation test cases. Acta Acoust. 88(4), 463–471 (2002)Google Scholar
  45. 45.
    Poinsot, T.J., Lele, S.K.: Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101, 104–129 (1992). MathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    André, B.: Etude expérimentale de l’effet du vol sur le bruit de choc de jets supersoniques sous-détendus. PhD Thesis, L’École Centrale de Lyon (2012)Google Scholar
  47. 47.
    Ffowcs Williams, J.E., Hawkings, D.L.: Sound generation by turbulence and surfaces in arbitrary motion. Philos. Trans. R. Soc. Lond. 264(1151), 321–342 (1969). CrossRefzbMATHGoogle Scholar
  48. 48.
    Farassat, F.: Derivation of formulations 1 and 1A of Farassat. Technical Memorandum 2007-214853, NASA (2007)Google Scholar
  49. 49.
    Tam, C.K.W.: Broadband shock-associated noise of moderately imperfectly expanded supersonic jets. J. Sound Vib. 140(1), 55–71 (1990). MathSciNetCrossRefzbMATHGoogle Scholar
  50. 50.
    Lui, C.C.M.: A numerical investigation of shock-associated noise. PhD Thesis, Stanford University (2003)Google Scholar
  51. 51.
    Andersson, N., Eriksson, L.E., Davidson, L.: A study of Mach 0.75 jets and their radiated sound using large-eddy simulation. In: 10th AIAA/CEAS Aeroacoustics Conference, May 10–12, Manchester, AIAA Paper 2004-3024 (2004).
  52. 52.
    Tam, C.K.W.: Broadband shock associated noise from supersonic jets measured by a ground observer. AIAA J. 30(10), 2395–2401 (1992). CrossRefGoogle Scholar
  53. 53.
    Pérez Arroyo, C., Daviller, G., Puigt, G., Airiau, C.: Hydrodynamic–acoustic filtering of a supersonic under-expanded jet. In: Grigoriadis, D., Geurts, B., Kuerten, H., Fröhlich, J., Armenio, V. (eds.) Direct and Large-Eddy Simulation X, pp. 79–84. Springer, Cham (2018). CrossRefGoogle Scholar
  54. 54.
    Tinney, C.E., Jordan, P.: The near pressure field of co-axial subsonic jets. J. Fluid Mech. 611, 175–204 (2008). CrossRefzbMATHGoogle Scholar
  55. 55.
    Savarese, A., Jordan, P., Girard, S., Royer, A., Fourment, C., Collin, E., Gervais, Y., Porta, M.: Experimental study of shock-cell noise in underexpanded supersonic jets. In: 19th AIAA/CEAS Aeroacoustics Conference, Aeroacoustics Conferences, 27–29 May, Berlin, AIAA Paper 2013-2080 (2013).
  56. 56.
    Daviller, G., Lehnasch, G., Jordan, P.: Numerical investigation of the influence of upstream conditions on properties of shock noise in shock/mixing layer interaction. In: International Symposium of Turbulence and Shear Flow Phenomena, vol. 1 (2013)Google Scholar
  57. 57.
    Pérez Arroyo, C.: Large eddy simulations of a dual-stream jet with shockcells and noise emission analysis. PhD Thesis, CERFACS and Institut National Polytechnique de Toulouse (2016)Google Scholar
  58. 58.
    Suda, H., Manning, T.A., Kaji, S.: Transition of oscillation modes of rectangular supersonic jet in screech. In: 15th AIAA Aeroacoustics Conference, 25–27 October, Long Beach, California, AIAA Paper 1993-4323 (1993).
  59. 59.
    André, B., Castelain, T., Bailly, C.: Experimental study of flight effects on screech in underexpanded jets. Phys. Fluids 23(12), 1–14 (2011). CrossRefGoogle Scholar
  60. 60.
    Ray, P.K., Lele, S.K.: Sound generated by instability wave/shock-cell interaction in supersonic jets. J. Fluid Mech. 587, 173–215 (2007). MathSciNetCrossRefzbMATHGoogle Scholar
  61. 61.
    Guariglia, D.: Shock-cell noise investigation on a subsonic/supersonic coaxial jet. PhD Thesis, von Karman Institute for Fluid Dynamics and Università Degli Study di Roma, La Sapienza (2017)Google Scholar
  62. 62.
    Singh, A., Chatterjee, A.: Numerical prediction of supersonic jet screech frequency. Shock Waves 17(4), 263–272 (2007). CrossRefzbMATHGoogle Scholar
  63. 63.
    Shur, M.L., Spalart, P.R., Strelets, M.K.: Noise prediction for underexpanded jets in static and flight conditions. AIAA J. 49(9), 2000–2017 (2011). CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringSherbrooke UniversitySherbrookeCanada
  2. 2.CERFACSToulouseFrance
  3. 3.ONERAToulouseFrance
  4. 4.IMFT, CNRSUniversité de ToulouseToulouseFrance

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