Intermittent statistics of the 0-mode pressure fluctuations in the near field of Mach 0.9 circular jets at low and high Reynolds numbers

Abstract

The present paper reports an investigation of the statistical properties of pressure fluctuations in the near field of subsonic compressible jets. The data-base analyzed has been obtained numerically by DNS and LES of two single-stream circular jets, having diameter-based Reynolds numbers of 3125 and 100,000 and Mach number 0.9, respectively, initially laminar and highly disturbed. Pressure fluctuations are extracted from several virtual probes positioned in the near field of the jets and covering a region from 0 to 20 diameters in the axial direction and from 0.5 to 3 diameters in the radial. An azimuthal decomposition of the pressure fluctuations is performed, and the statistical analysis is applied to the axisymmetric 0-mode component and compared to the results obtained from the full original signals. The intermittent behavior is investigated by the estimation of standard statistical indicators, such as probability distribution functions and flatness factor, as well as through conditional statistics based on the application of the wavelet transform. It is shown that downstream of the potential core, intermittency estimated through the traditional indicators is relevant even at the lowest Re for the full signals, whereas it is apparently not significant for the 0-mode component. The wavelet analysis provides an estimation of intermittency scale-by-scale and allows for the calculation of a frequency-dependent FF. This approach reveals that the 0-mode component has a relevant degree of intermittency around the frequencies associated with the Kelvin–Helmholtz instability. The statistics of the intermittent events, in terms of their temporal appearance and energy content, are shown to be weakly sensitive to the jet Reynolds number and the universal behavior can be reproduced by simple stochastic models.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

References

  1. 1.

    Lighthill, M.J.: On sound generated aerodynamically. I. General theory. Proc. R. Soc. A Math. Phys. Eng. Sci. 211, 564–587 (1952)

    MathSciNet  MATH  Google Scholar 

  2. 2.

    Lighthill, M.J.: On sound generated aerodynamically. II. Turbulence as a source of sound. Proc. R. Soc. A Math. Phys. Eng. Sci. 222, 1–32 (1954)

    MathSciNet  MATH  Google Scholar 

  3. 3.

    Mollo-Christensen, E., Koplin, M.A., Martuccelli, J.R.: Experiments on jet flows and jet noise far-field spectra and directivity patterns. J. Fluid Mech. 18, 285–301 (1964)

    MATH  Article  Google Scholar 

  4. 4.

    Tam, K.W., Golebiowski, M., Seiner, J.M.: On the two components of turbulent mixing noise from supersonic jets. AIAA Paper 96–1716, 2nd AIAA-CEAS Aeroacoustic Conference, Stae College (PA), May 6-8 (1996)

  5. 5.

    Karabasov, S.A.: Understanding jet noise. Philos. Trans. R. Soc. A 368, 3593–3608 (2010)

    MathSciNet  MATH  Article  Google Scholar 

  6. 6.

    Tam, C.K.W., Viswanathan, K., Ahuja, K.K., Panda, J.: The sources of jet noise: experimental evidence. J. Fluid Mech. 615, 253–292 (2008)

    MATH  Article  Google Scholar 

  7. 7.

    Jordan, P., Colonius, T.: Wave packets and turbulent jet noise. Annu. Rev. Fluid Mech. 45, 17–195 (2013)

    MathSciNet  MATH  Article  Google Scholar 

  8. 8.

    Crow, S. C.: Acoustic gain of a turbulent jet. In: Physical Society Meeting, University of Colorado, Boulder, Paper IE, vol. 6 (1972)

  9. 9.

    Crighton, D.G., Huerre, P.: Shear-layer pressure fluctuations and superdirective acoustic sources. J. Fluid Mech. 220, 355–368 (1990)

    MATH  Article  Google Scholar 

  10. 10.

    Cavalieri, A.V.G., Jordan, P., Colonius, T., Gervais, Y.: Axisymmetric superdirectivity in subsonic jets. J. Fluid Mech. 704, 388–420 (2012)

    MathSciNet  MATH  Article  Google Scholar 

  11. 11.

    Léon, O., Brazier, J. -P.: Investigation of the near and far pressure fields of dual-stream jets using an Euler-based PSE model. In: 19th AIAA/CEAS Aeroacoustics Conference and Exhibit (2013)

  12. 12.

    Sinha, A., Rodrìguez, D., Brés, G.A., Colonius, T.: Wavepacket models for supersonic jet noise. J. Fluid Mech. 742, 71–95 (2014)

    Article  Google Scholar 

  13. 13.

    Cavalieri, A.V.G., Rodríguez, D., Jordan, P., Colonius, T., Gervais, Y.: Wave packets in the velocity field of turbulent jets. J. Fluid Mech. 730, 559–592 (2013)

    MathSciNet  MATH  Article  Google Scholar 

  14. 14.

    Zhang, M., Jordan, P., Lehnasch, G., Cavalieri, A.V.G., Aggarwal, A.: Just enough jitter for jet noise? AIAA Paper 2014–3061, 20th AIAA-CEAS Aerocoustic Conference, Atlanta (GE), June 16-20 (2014)

  15. 15.

    Tissot, G., Zhang, M., Lajus Jr., F.C., Cavalieri, A.V.G., Jordan, P.: Sensitivity of wavepackets to nonlinear effects: the role of the critical layer. J. Fluid Mech. 811, 9–137 (2017)

    MathSciNet  MATH  Article  Google Scholar 

  16. 16.

    Juvé, D., Sunyach, M., Comte-Bellot, G.: Intermittency of the noise emission in subsonic cold jets. J. Sound Vib. 71, 319–32 (1980)

    Article  Google Scholar 

  17. 17.

    Guj, G., Carley, M., Camussi, R.: Acoustic identification of coherent structures in a turbulent jet. J. Sound Vib. 259, 1037–1065 (2003)

    Article  Google Scholar 

  18. 18.

    Hileman, J.I., Thurow, B.S., Caraballo, E.J., Samimy, M.: Large-scale structure evolution and sound emission in high-speed jets: real-time visualization with simultaneous acoustic measurements. J. Fluid Mech. 544, 277–307 (2005)

    MATH  Article  Google Scholar 

  19. 19.

    Bogey, C., Bailly, C.: An analysis of the correlations between the turbulent flow and the sound pressure fields of subsonic jets. J. Fluid Mech. 583, 71–97 (2007)

    MATH  Article  Google Scholar 

  20. 20.

    Kastner, J., Samimy, M., Hileman, J., Freund, J.B.: Comparison of noise mechanisms in high and low Reynolds number high-speed jets. AIAA J. 44, 225–2258 (2006)

    Article  Google Scholar 

  21. 21.

    Suponitsky, V., Sandham, N.D., Morfey, C.L.: Linear and nonlinear mechanisms of sound radiation by instability waves in subsonic jets. J. Fluid Mech. 658, 509–538 (2010)

    MATH  Article  Google Scholar 

  22. 22.

    Bogey, C., Bailly, C., Juvé, D.: Noise investigation of a high subsonic, moderate Reynolds number jet using a compressible LES. Theor. Comput. Fluid Dyn. 16(4), 273–297 (2003)

    MATH  Article  Google Scholar 

  23. 23.

    Crighton, D.G., Gaster, M.: Stability of slowly diverging jet flow. J. Fluid Mech. 77, 397–413 (1976)

    MATH  Article  Google Scholar 

  24. 24.

    Schmidt, O.T., Towne, A., Rigas, G., Colonius, T., Brès, G.A.: Spectral analysis of jet turbulence. J. Fluid Mech. 855, 953–982 (2018)

    MathSciNet  MATH  Article  Google Scholar 

  25. 25.

    Cavalieri, A.V.G., Jordan, P., Agarwal, A., Gervais, Y.: Jittering wave-packet models for subsonic jet noise. J. Sound Vib. 330, 447–4492 (2011)

    Google Scholar 

  26. 26.

    Cavalieri, A.V.G., Jordan, P., Lesshafft, L.: Wave-packet models for jet dynamics and sound radiation. Appl. Mech. Rev. 71, 020802 (2019)

    Article  Google Scholar 

  27. 27.

    Cavalieri, A.V.G., Agarwal, A.: Coherence decay and its impact on sound radiation by wavepackets. J. Fluid Mech. 748, 399–415 (2014)

    MathSciNet  MATH  Article  Google Scholar 

  28. 28.

    Baqui, Y.B., Agarwal, A., Cavalieri, A.V.G., Sinayoko, S.: A coherence-matched linear mechanism for subsonic jets. J. Fluid Mech. 776, 235–267 (2015)

    Article  Google Scholar 

  29. 29.

    Maia, I.A., Jordan, P., Cavalieri, A.V.G., Jaunet, V.: Two-point wavepacket modelling of jet noise. Proc. R. Soc. A 475, 20190199 (2019)

    MathSciNet  Article  Google Scholar 

  30. 30.

    Jaunet, V., Jordan, P., Cavalieri, A.V.G.: Two-point coherence of wavepackets in turbulent jets. Physical Review Fluids 2, 024604 (2017)

    Article  Google Scholar 

  31. 31.

    Breakey, D., Jordan, P., Cavalieri, A.V.G., Nogueira, P., Léon, O., Colonius, T., Rodríguez, D.: Experimental study of turbulent-jet wave packets and their acoustic efficiency. Phys. Rev. Fluids 2, 124601 (2017)

    Article  Google Scholar 

  32. 32.

    Kopiev, V., Chernyshev, S.: Simulation of azimuthal characteristics of turbulent jet noise by correlation model of quadrupole noise sources. Int. J. Aeroacoust. 13(1), 39–60 (2014)

    Article  Google Scholar 

  33. 33.

    Kopiev, V., Faranosov, G.: On defining the jet noise source quadrupole structure on the basis of multiarray acoustic data and correlation theory. AIAA paper AIAA 2016-2806, 22nd AIAA/CEAS Aeroacoustics Conference, May 30–June 1, Lyon, France (2016)

  34. 34.

    Kearney-Fischer, M., Sinha, A., Samimy, M.: Intermittent nature of subsonic jet noise. AIAA J. 51, 1142–1155 (2013)

    Article  Google Scholar 

  35. 35.

    Kearney-Fischer, M.: A model function for jet noise events at aft angles and what it says about the statistical relationships of the events. J. Sound Vib. 338, 217–236 (2015)

    Article  Google Scholar 

  36. 36.

    Camussi, R., Di Marco, A., Castelain, T.: Statistical analysis of the hydrodynamic pressure in the near field of compressible jets. Int. J. Heat Fluid Flow 64, 1–9 (2017a)

    Article  Google Scholar 

  37. 37.

    Camussi, R., Mancinelli, M., Di Marco, A.: Intermittency and stochastic modeling of hydrodynamic pressure fluctuations in the near field of compressible jets. Int. J. Heat Fluid Flow 68, 180–188 (2017b)

    Article  Google Scholar 

  38. 38.

    Bogey, C.: Two-dimensional features of correlations in the flow and near pressure fields of Mach number 0.9 jets. AIAA Paper 2019-0806, AIAA SciTech Forum, San Diego (CA), Jan 7-11 (2019)

  39. 39.

    Bogey, C., Marsden, O., Bailly, C.: Large-eddy simulation of the flow and acoustic fields of a Reynolds number 10e5 subsonic jet with tripped exit boundary layers. Phys. Fluids 23, 035104 (2011)

    Article  Google Scholar 

  40. 40.

    Bogey, C.: Grid sensitivity of flow field and noise of high-Reynolds-number jets computed by large-eddy simulation. Int. J. Aeroacoust. 17, 399–424 (2018)

    Article  Google Scholar 

  41. 41.

    Bogey, C., Sabatini, R.: Effects of nozzle-exit boundary-layer profile on the initial shear-layer instability, flow field and noise of subsonic jets. J. Fluid Mech. 876, 288–325 (2019)

    MATH  Article  Google Scholar 

  42. 42.

    Michalke, A., Fuchs, H.V.: On turbulence and noise of an axisymmetric shear flow. J. Fluid Mech. 70(1), 179–205 (1975)

    MATH  Article  Google Scholar 

  43. 43.

    Arndt, R.E.A., Long, D.F., Glauser, M.N.: The proper orthogonal decomposition of pressure fluctuations surrounding a turbulent jet. J. Fluid Mech. 340, 1–33 (1997)

    Article  Google Scholar 

  44. 44.

    Jung, D., Gamard, S., George, W.K.: Downstream evolution of the most energetic modes in a turbulent axisymmetric jet at high Reynolds number. Part 1. The near-field region. J. Fluid Mech. 514, 173–204 (2004)

    MATH  Article  Google Scholar 

  45. 45.

    Juve, D., Sunyach, M., Comte-Bellot, G.: Filtered azimuthal correlations in the acoustic far field of a subsonic jet. AIAA J. 17(1), 112–113 (1979). https://doi.org/10.2514/3.61076

    Article  Google Scholar 

  46. 46.

    Farge, M.: Wavelet transforms and their applications to turbulence. Ann. Rev. Fluid Mech. 24, 395–458 (1992)

    MathSciNet  MATH  Article  Google Scholar 

  47. 47.

    Torrence, C., Compo, G.P.: A practical guide to wavelet analysis. Bull. Am. Meteorol. Soc. 79, 61–78 (1998)

    Article  Google Scholar 

  48. 48.

    Auger, F., Flandrin, P., Goncalves, P., Lemoine, O.: Time-Frequency Toolbox (2005). http://tftb.nongnu.org/

  49. 49.

    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)

    MathSciNet  MATH  Article  Google Scholar 

  50. 50.

    Camussi, R., Guj, G.: Orthonormal wavelet decomposition of turbulent flows: intermittency and coherent structures. J. Fluid Mech. 348, 17–199 (1997)

    MathSciNet  MATH  Article  Google Scholar 

  51. 51.

    Meneveau, C.: Analysis of turbulence in the orthonormal wavelet representation. J. Fluid Mech. 232, 469–520 (1991)

    MathSciNet  MATH  Article  Google Scholar 

  52. 52.

    Grizzi, S., Camussi, R.: Wavelet analysis of near-field pressure fluctuations generated by a subsonic jet. J. Fluid Mech. 698, 93–124 (2012)

    MATH  Article  Google Scholar 

  53. 53.

    Suzuki, T.M., Colonius, T.: Instability waves in a subsonic round jet detected using a near-field phased microphone array. J. Fluid Mech. 565, 197–226 (2007)

    MATH  Article  Google Scholar 

  54. 54.

    Métais, O., Lesieur, M.: Spectral large-eddy simulations of isotropic and stably-stratified turbulence. J. Fluid Mech. 239, 157–194 (1992)

    MathSciNet  MATH  Article  Google Scholar 

  55. 55.

    Holzer, M., Siggia, E.: Skewed, exponential pressure distributions from Gaussian velocities. Phys. Fluids A 5, 2525 (1993)

    MATH  Article  Google Scholar 

  56. 56.

    Cao, N., Chen, S., Doolen, G.D.: Statistics and structures of pressure in isotropic turbulence. Phys. Fluids 11, 2235–2250 (1999)

    MathSciNet  MATH  Article  Google Scholar 

  57. 57.

    Feller, E.: An Introduction to Probability Theory and Its Applications. Wiley, Hoboken (1971)

    Google Scholar 

  58. 58.

    Mollo-Christensen, E.: Measurements of near field pressure of subsonic jets. Technical report, DTCI, (1963)

  59. 59.

    Mollo-Christensen, E.: Jet noise and shear flow instability seen from an experimenter’s viewpoint. J. Appl. Mech. 34, 1–7 (1967)

    Article  Google Scholar 

  60. 60.

    Bogey, C., Pineau, P.: Potential-core closing of temporally developing jets at Mach numbers between 0.3 and 2: scaling and conditional averaging of flow and sound fields. Phys. Rev. Fluids 124601, 1–25 (2019)

    Google Scholar 

  61. 61.

    Pineau, P., Bogey, C.: Steepened Mach waves near supersonic jets: study of azimuthal structure and generation process using conditional averages. J. Fluid Mech. 880, 594–619 (2019)

    MathSciNet  MATH  Article  Google Scholar 

  62. 62.

    Bogey, C.: On noise generation in low Reynolds number temporal round jets at a Mach number of 0.9. J. Fluid Mech. 859, 1022–1056 (2019)

    MathSciNet  MATH  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to R. Camussi.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Communicated by Sergio Pirozzoli.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Camussi, R., Bogey, C. Intermittent statistics of the 0-mode pressure fluctuations in the near field of Mach 0.9 circular jets at low and high Reynolds numbers. Theor. Comput. Fluid Dyn. (2021). https://doi.org/10.1007/s00162-020-00553-9

Download citation

Keywords

  • Jet noise
  • Intermittency
  • Stochastic modeling