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.
Similar content being viewed by others
References
Lighthill, M.J.: On sound generated aerodynamically. I. General theory. Proc. R. Soc. A Math. Phys. Eng. Sci. 211, 564–587 (1952)
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)
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)
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)
Karabasov, S.A.: Understanding jet noise. Philos. Trans. R. Soc. A 368, 3593–3608 (2010)
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)
Jordan, P., Colonius, T.: Wave packets and turbulent jet noise. Annu. Rev. Fluid Mech. 45, 17–195 (2013)
Crow, S. C.: Acoustic gain of a turbulent jet. In: Physical Society Meeting, University of Colorado, Boulder, Paper IE, vol. 6 (1972)
Crighton, D.G., Huerre, P.: Shear-layer pressure fluctuations and superdirective acoustic sources. J. Fluid Mech. 220, 355–368 (1990)
Cavalieri, A.V.G., Jordan, P., Colonius, T., Gervais, Y.: Axisymmetric superdirectivity in subsonic jets. J. Fluid Mech. 704, 388–420 (2012)
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)
Sinha, A., Rodrìguez, D., Brés, G.A., Colonius, T.: Wavepacket models for supersonic jet noise. J. Fluid Mech. 742, 71–95 (2014)
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)
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)
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)
Juvé, D., Sunyach, M., Comte-Bellot, G.: Intermittency of the noise emission in subsonic cold jets. J. Sound Vib. 71, 319–32 (1980)
Guj, G., Carley, M., Camussi, R.: Acoustic identification of coherent structures in a turbulent jet. J. Sound Vib. 259, 1037–1065 (2003)
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)
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)
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)
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)
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)
Crighton, D.G., Gaster, M.: Stability of slowly diverging jet flow. J. Fluid Mech. 77, 397–413 (1976)
Schmidt, O.T., Towne, A., Rigas, G., Colonius, T., Brès, G.A.: Spectral analysis of jet turbulence. J. Fluid Mech. 855, 953–982 (2018)
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)
Cavalieri, A.V.G., Jordan, P., Lesshafft, L.: Wave-packet models for jet dynamics and sound radiation. Appl. Mech. Rev. 71, 020802 (2019)
Cavalieri, A.V.G., Agarwal, A.: Coherence decay and its impact on sound radiation by wavepackets. J. Fluid Mech. 748, 399–415 (2014)
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)
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)
Jaunet, V., Jordan, P., Cavalieri, A.V.G.: Two-point coherence of wavepackets in turbulent jets. Physical Review Fluids 2, 024604 (2017)
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)
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)
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)
Kearney-Fischer, M., Sinha, A., Samimy, M.: Intermittent nature of subsonic jet noise. AIAA J. 51, 1142–1155 (2013)
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)
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)
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)
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)
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)
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)
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)
Michalke, A., Fuchs, H.V.: On turbulence and noise of an axisymmetric shear flow. J. Fluid Mech. 70(1), 179–205 (1975)
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)
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)
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
Farge, M.: Wavelet transforms and their applications to turbulence. Ann. Rev. Fluid Mech. 24, 395–458 (1992)
Torrence, C., Compo, G.P.: A practical guide to wavelet analysis. Bull. Am. Meteorol. Soc. 79, 61–78 (1998)
Auger, F., Flandrin, P., Goncalves, P., Lemoine, O.: Time-Frequency Toolbox (2005). http://tftb.nongnu.org/
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)
Camussi, R., Guj, G.: Orthonormal wavelet decomposition of turbulent flows: intermittency and coherent structures. J. Fluid Mech. 348, 17–199 (1997)
Meneveau, C.: Analysis of turbulence in the orthonormal wavelet representation. J. Fluid Mech. 232, 469–520 (1991)
Grizzi, S., Camussi, R.: Wavelet analysis of near-field pressure fluctuations generated by a subsonic jet. J. Fluid Mech. 698, 93–124 (2012)
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)
Métais, O., Lesieur, M.: Spectral large-eddy simulations of isotropic and stably-stratified turbulence. J. Fluid Mech. 239, 157–194 (1992)
Holzer, M., Siggia, E.: Skewed, exponential pressure distributions from Gaussian velocities. Phys. Fluids A 5, 2525 (1993)
Cao, N., Chen, S., Doolen, G.D.: Statistics and structures of pressure in isotropic turbulence. Phys. Fluids 11, 2235–2250 (1999)
Feller, E.: An Introduction to Probability Theory and Its Applications. Wiley, Hoboken (1971)
Mollo-Christensen, E.: Measurements of near field pressure of subsonic jets. Technical report, DTCI, (1963)
Mollo-Christensen, E.: Jet noise and shear flow instability seen from an experimenter’s viewpoint. J. Appl. Mech. 34, 1–7 (1967)
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)
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)
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)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Sergio Pirozzoli.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
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. 35, 229–247 (2021). https://doi.org/10.1007/s00162-020-00553-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00162-020-00553-9