Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-21T11:34:02.829Z Has data issue: false hasContentIssue false

Acoustic tones in the near-nozzle region of jets: characteristics and variations between Mach numbers 0.5 and 2

Published online by Cambridge University Press:  25 June 2021

Christophe Bogey*
Laboratoire de Mécanique des Fluides et d'Acoustique, Univ Lyon, CNRS, Ecole Centrale de Lyon, INSA Lyon, Univ Claude Bernard Lyon I, UMR 5509, 69130Ecully, France
Email address for correspondence:


The characteristics of acoustic tones near the nozzle of jets are investigated for Mach numbers between ${M}=0.50$ and 2 using large-eddy simulations. Peaks are observed in all cases. They are tonal for ${M}\geq 0.75$ and broaden for lower Mach numbers. They are associated with the azimuthal modes $n_{\theta }=0$ to $n_{\theta }^{max}$, with $n_{\theta }^{max}=8$ for ${M}=0.75$ and 1 for ${M}=2$, for example. Their frequencies do not appreciably vary with the nozzle-exit boundary-layer thickness and turbulence and fall in the frequency bands predicted for the upstream-propagating guided jet waves using a vortex-sheet model. For all azimuthal modes, the peak intensities are highest for the first radial guided jet mode. They increase approximately as ${M}^8$ for ${M}\leq 1$ and as ${M}^3$ for ${M}\geq 1$, following the scaling laws of jet noise, suggesting that they mainly result from a band-pass filtering of the upstream-travelling sound waves by the guided jet modes. In support of this, the Mach number variations of the peak width and sharpness are explained by the eigenfunctions of the guided waves. Moreover, it appears that, for high subsonic Mach numbers, among the waves possibly resonating in the potential core, only those close to the cutoff frequencies of the guided jet modes can contribute to the near-nozzle peaks. Finally, the peaks are detectable in the far field for large radiation angles. For ${M}= 0.90$, for instance, they emerge for angles higher than $135^\circ$.

JFM Papers
© The Author(s), 2021. Published by 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.)



Ahuja, K.K., Tester, B.J. & Tanna, H.K. 1987 Calculation of far field jet noise spectra from near field measurements with true source location. J. Sound Vib. 116 (3), 415426.CrossRefGoogle Scholar
Arndt, R.E.A., Long, D.F. & Glauser, M.N. 1997 The proper orthogonal decomposition of pressure fluctuations surrounding a turbulent jet. J. Fluid Mech. 340, 133.CrossRefGoogle Scholar
Berland, J., Bogey, C., Marsden, O. & Bailly, C. 2007 High-order, low dispersive and low dissipative explicit schemes for multiple-scale and boundary problems. J. Comput. Phys. 224 (2), 637662.CrossRefGoogle Scholar
Bogey, C. 2018 Grid sensitivity of flow field and noise of high-Reynolds-number jets computed by large-eddy simulation. Intl J. Aeroacoust. 17 (4-5), 399424.CrossRefGoogle Scholar
Bogey, C. 2021 Generation of excess noise by jets with highly disturbed laminar boundary-layer profiles. AIAA J. 59 (2), 569579.CrossRefGoogle Scholar
Bogey, C. & Bailly, C. 2004 A family of low dispersive and low dissipative explicit schemes for flow and noise computations. J. Comput. Phys. 194 (1), 194214.CrossRefGoogle Scholar
Bogey, C. & Bailly, C. 2006 Large eddy simulations of transitional round jets: influence of the Reynolds number on flow development and energy dissipation. Phys. Fluids 18 (6), 065101.CrossRefGoogle Scholar
Bogey, C. & Bailly, C. 2010 Influence of nozzle-exit boundary-layer conditions on the flow and acoustic fields of initially laminar jets. J. Fluid Mech. 663, 507539.CrossRefGoogle Scholar
Bogey, C., Barré, S., Fleury, V., Bailly, C. & Juvé, D. 2007 Experimental study of the spectral properties of near-field and far-field jet noise. Intl J. Aeroacoust. 6 (2), 7392.CrossRefGoogle Scholar
Bogey, C., de Cacqueray, N. & Bailly, C. 2009 A shock-capturing methodology based on adaptative spatial filtering for high-order non-linear computations. J. Comput. Phys. 228 (5), 14471465.CrossRefGoogle Scholar
Bogey, C., de Cacqueray, N. & Bailly, C. 2011 Finite differences for coarse azimuthal discretization and for reduction of effective resolution near origin of cylindrical flow equations. J. Comput. Phys. 230 (4), 11341146.CrossRefGoogle Scholar
Bogey, C. & Gojon, R. 2017 Feedback loop and upwind-propagating waves in ideally-expanded supersonic impinging round jets. J. Fluid Mech. 823, 562591.CrossRefGoogle Scholar
Bogey, C. & Marsden, O. 2016 Simulations of initially highly disturbed jets with experiment-like exit boundary layers. AIAA J. 54 (4), 12991312.CrossRefGoogle Scholar
Bogey, C., Marsden, O. & Bailly, C. 2011 a Large-eddy simulation of the flow and acoustic fields of a Reynolds number $10^5$ subsonic jet with tripped exit boundary layers. Phys. Fluids 23 (3), 035104.CrossRefGoogle Scholar
Bogey, C., Marsden, O. & Bailly, C. 2011 b On the spectra of nozzle-exit velocity disturbances in initially nominally turbulent, transitional jets. Phys. Fluids 23 (9), 091702.CrossRefGoogle Scholar
Bogey, C., Marsden, O. & Bailly, C. 2012 Influence of initial turbulence level on the flow and sound fields of a subsonic jet at a diameter-based Reynolds number of $10^5$. J. Fluid Mech. 701, 352385.CrossRefGoogle Scholar
Bogey, C. & Sabatini, R. 2019 Effects of nozzle-exit boundary-layer profile on the initial shear-layer instability, flow field and noise of subsonic jets. J. Fluid Mech. 876, 288325.CrossRefGoogle Scholar
Brès, G.A., Jordan, P., Jaunet, V., Le Rallic, M., Cavalieri, A.V.G., Towne, A., Lele, S.K., Colonius, T. & Schmidt, O.T. 2018 Importance of the nozzle-exit boundary-layer state in subsonic turbulent jets. J. Fluid Mech. 851, 83124.CrossRefGoogle Scholar
Brès, G.A. & Lele, S.K. 2019 Modelling of jet noise: a perspective from large-eddy simulations. Phil. Trans. R. Soc. A 377 (2159), 20190081.CrossRefGoogle ScholarPubMed
Bridges, J. & Brown, C.A. 2005 Validation of the small hot jet acoustic rig for aeroacoustic research. AIAA Paper 2005-2846.CrossRefGoogle Scholar
Brown, G.L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64 (4), 775816.CrossRefGoogle Scholar
Cavalieri, A.V.G., Jordan, P., Colonius, T. & Gervais, Y. 2012 Axisymmetric superdirectivity in subsonic jets. J. Fluid Mech. 704, 388420.CrossRefGoogle Scholar
Colonius, T., Lele, S.K. & Moin, P. 1997 Sound generation in a mixing layer. J. Fluid Mech. 330, 375409.CrossRefGoogle Scholar
Edgington-Mitchell, D. 2019 Aeroacoustic resonance and self-excitation in screeching and impinging supersonic jets - a review. Intl J. Aeroacoust. 18 (2-3), 118188.CrossRefGoogle Scholar
Edgington-Mitchell, D., Jaunet, V., Jordan, P., Towne, A., Soria, J. & Honnery, D. 2018 Upstream-travelling acoustic jet modes as a closure mechanism for screech. J. Fluid Mech. 855, R1.CrossRefGoogle Scholar
Edgington-Mitchell, D., Wang, T., Nogueira, P., Schmidt, O., Jaunet, V., Duke, D., Jordan, P. & Towne, A. 2021 Waves in screeching jets. J. Fluid Mech. 913, A7.CrossRefGoogle Scholar
Fauconnier, D., Bogey, C. & Dick, E. 2013 On the performance of relaxation filtering for large-eddy simulation. J. Turbul. 14 (1), 2249.CrossRefGoogle Scholar
Ffowcs Williams, J.E. 1963 The noise from turbulence convected at high speed. Phil. Trans. R. Soc. Lond. A 255 (1061), 469503.Google Scholar
Ffowcs Williams, J.E., Simson, J. & Virchis, V.J. 1975 ‘Crackle’: an annoying component of jet noise. J. Fluid Mech. 71 (2), 251271.CrossRefGoogle Scholar
Gojon, R., Bogey, C. & Marsden, O. 2016 Investigation of tone generation in ideally expanded supersonic planar impinging jets using large-eddy simulation. J. Fluid Mech. 808, 90115.CrossRefGoogle Scholar
Gojon, R., Bogey, C. & Mihaescu, M. 2018 Oscillation modes in screeching jets. AIAA J. 56 (7), 29182924.CrossRefGoogle Scholar
Gutmark, E. & Ho, C.-M. 1983 Preferred modes and the spreading rates of jets. Phys. Fluids 26 (10), 29322938.CrossRefGoogle Scholar
Ho, C.-M. & Huang, L.-S. 1982 Subharmonics and vortex merging in mixing layers. J. Fluid Mech. 119, 443473.CrossRefGoogle Scholar
Ho, C.M. & Nosseir, N.S. 1981 Dynamics of an impinging jet. Part 1. The feedback phenomenon. J. Fluid Mech. 105, 119142.CrossRefGoogle Scholar
Jaunet, V., Jordan, P., Cavalieri, A.V.G., Towne, A., Colonius, T., Schmidt, O. & Brès, G.A. 2016 Tonal dynamics and sound in free and installed turbulent jets. AIAA Paper 2016-3016.Google Scholar
Jaunet, V., Mancinelli, M., Jordan, P., Towne, A., Edgington-Mitchell, D.M., Lehnasch, G. & Girard, S. 2019 Dynamics of round jet impingement. AIAA Paper 2019-2769.CrossRefGoogle Scholar
Jordan, P., Jaunet, V., Towne, A., Cavalieri, A.V.G., Colonius, T., Schmidt, O. & Agarwal, A. 2018 Jet–flap interaction tones. J. Fluid Mech. 853, 333358.CrossRefGoogle Scholar
Juvé, D., Sunyach, M. & Comte-Bellot, G. 1979 Filtered azimuthal correlations in the acoustic far field of a subsonic jet. AIAA J. 17 (1), 112113.CrossRefGoogle Scholar
Kremer, F. & Bogey, C. 2015 Large-eddy simulation of turbulent channel flow using relaxation filtering: resolution requirement and Reynolds number effects. Comput. Fluids 116, 1728.CrossRefGoogle Scholar
Lau, J.C., Morris, P.J. & Fisher, M.J. 1979 Measurements in subsonic and supersonic free jets using a laser velocimeter. J. Fluid Mech. 93 (1), 127.CrossRefGoogle Scholar
Laufer, J. & Monkewitz, P. 1980 On turbulent jet flows: a new perspective. AIAA Paper 80-0962.CrossRefGoogle Scholar
Laufer, J., Schlinker, R. & Kaplan, R.E. 1976 Experiments on supersonic jet noise. AIAA J. 14 (4), 489497.CrossRefGoogle Scholar
Li, X., Zhang, X., Hao, P. & He, F. 2020 Acoustic feedback loops for screech tones of underexpanded free round jets at different modes. J. Fluid Mech. 902, A17.CrossRefGoogle Scholar
Lighthill, M.J. 1952 On sound generated aerodynamically I. General theory. Proc. R. Soc. A 211 (1107), 564587.Google Scholar
Lyrintzis, A.S. & Coderoni, M. 2020 Overview of the use of large-eddy simulations in jet aeroacoustics. AIAA J. 58 (4), 16201638.CrossRefGoogle Scholar
Mancinelli, M., Jaunet, V., Jordan, P. & Towne, A. 2019 Screech-tone prediction using upstream-travelling jet modes. Exp. Fluids 60 (1), 22.CrossRefGoogle Scholar
Michalke, A. 1984 Survey on jet instability theory. Prog. Aerosp. Sci. 21, 159199.CrossRefGoogle Scholar
Mohseni, K. & Colonius, T. 2000 Numerical treatment of polar coordinate singularities. J. Comput. Phys. 157 (2), 787795.CrossRefGoogle Scholar
Mollo-Christensen, E., Kolpin, M.A. & Martucelli, J.R. 1964 Experiments on jet flows and jet noise far-field spectra and directivity patterns. J. Fluid Mech. 18 (2), 285301.CrossRefGoogle Scholar
Morris, P.J. 2010 The instability of high speed jets. Intl J. Aeroacoust. 9 (1-2), 150.CrossRefGoogle Scholar
Powell, A. 1953 On edge tones and associated phenomena. Acta Acust. United Ac. 3 (4), 233243.Google Scholar
Raman, G. 1998 Advances in understanding supersonic jet screech: review and perpective. Prog. Aerosp. Sci. 34 (1), 45106.CrossRefGoogle Scholar
Schmidt, O., Towne, A., Colonius, T., Cavalieri, A.V.G., Jordan, P. & Brès, G.A. 2017 Wavepackets and trapped acoustic modes in a turbulent jet: coherent structure eduction and global stability. J. Fluid Mech. 825, 11531181.CrossRefGoogle Scholar
Shen, H. & Tam, C.K.W. 2002 Three-dimensional numerical simulation of the jet screech phenomenon. AIAA J. 40 (1), 3341.CrossRefGoogle Scholar
Suzuki, T. & Colonius, T. 2006 Instability waves in a subsonic round jet detected using a near-field phased microphone array. J. Fluid Mech. 565, 197226.CrossRefGoogle Scholar
Tam, C.K.W. 1998 Jet noise: since 1952. Theor. Comput. Fluid Dyn. 10 (1-4), 393405.CrossRefGoogle Scholar
Tam, C.K.W. & Ahuja, K.K. 1990 Theoretical model of discrete tone generation by impinging jets. J. Fluid Mech. 214, 6787.CrossRefGoogle Scholar
Tam, C.K.W. & Chandramouli, S. 2020 Jet-plate interaction tones relevant to over-the-wing engine mount concept. J. Sound Vib. 486, 115378.CrossRefGoogle 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), 175201.CrossRefGoogle Scholar
Tam, C.K.W. & Hu, F.Q. 1989 On the three families of instability waves of high-speed jets. J. Fluid Mech. 201, 447483.CrossRefGoogle Scholar
Tam, C.K.W. & Norum, T.D. 1992 Impingement tones of large aspect ratio supersonic rectangular jets. AIAA J. 30 (2), 304311.CrossRefGoogle Scholar
Towne, A., Cavalieri, A.V.G., Jordan, P., Colonius, T., Schmidt, O., Jaunet, V. & Brès, G.A. 2017 Acoustic resonance in the potential core of subsonic jets. J. Fluid Mech. 825, 11131152.CrossRefGoogle Scholar
Towne, A., Schmidt, O.T. & Brès, G.A. 2019 An investigation of the Mach number dependence of trapped acoustic waves in turbulent jets. AIAA Paper 2019-2546.CrossRefGoogle Scholar
Viswanathan, K. 2010 Distributions of noise sources in heated and cold jets: are they different? Intl J. Aeroacoust. 9 (4–5), 589625.CrossRefGoogle Scholar
Weightman, J.L., Amili, O., Honnery, D., Edgington-Mitchell, D. & Soria, J. 2019 Nozzle external geometry as a boundary condition for the azimuthal mode selection in an impinging underexpanded jet. J. Fluid Mech. 862, 421448.CrossRefGoogle Scholar
Whitham, G.B. 1974 Linear and Nonlinear Waves. John Wiley and Sons.Google Scholar
Winant, C. & Browand, F. 1974 Vortex pairing: the mechanism of turbulent mixing-layer growth at moderate reynolds number. J. Fluid Mech. 63 (2), 237255.CrossRefGoogle Scholar
Zaman, K.B.M.Q. 1985 Effect of initial condition on subsonic jet noise. AIAA J. 23 (9), 13701373.CrossRefGoogle Scholar
Zaman, K.B.M.Q. & Fagan, A.F. 2019 Near-exit pressure fluctuations in jets from circular and rectangular nozzles. NASA Tech. Rep. 2019-220383.Google Scholar
Zaman, K.B.M.Q., Fagan, A.F., Bridges, J.E. & Brown, C.A. 2015 An experimental investigation of resonant interaction of a rectangular jet with a flat plate. J. Fluid Mech. 779, 751775.CrossRefGoogle Scholar
Zaman, K.B.M.Q. & Hussain, A.K.M.F. 1981 Turbulence suppression in free shear flows by controlled excitation. J. Fluid Mech. 103, 133159.CrossRefGoogle Scholar