Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-15T23:23:36.722Z Has data issue: false hasContentIssue false
  • English
  • Français

Wavepacket modelling of broadband shock-associated noise in supersonic jets

Published online by Cambridge University Press:  05 May 2021

Marcus H. Wong Open the ORCID record for Marcus H. Wong [Opens in a new window] ,
Peter Jordan Open the ORCID record for Peter Jordan [Opens in a new window] ,
Igor A. Maia Open the ORCID record for Igor A. Maia [Opens in a new window] ,
André V.G. Cavalieri Open the ORCID record for André V.G. Cavalieri [Opens in a new window] ,
Rhiannon Kirby ,
Thales C.L. Fava  and
Daniel Edgington-Mitchell Open the ORCID record for Daniel Edgington-Mitchell [Opens in a new window]
Marcus H. Wong*
Affiliation:
Laboratory for Turbulence Research in Aerospace and Combustion, Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC3800, Australia
Peter Jordan
Affiliation:
Departement Fluides, Thermique, Combustion, Institut PPRIME, CNRS – Université de Poitiers – ENSMA, 86036Poitiers, France
Igor A. Maia
Affiliation:
Departement Fluides, Thermique, Combustion, Institut PPRIME, CNRS – Université de Poitiers – ENSMA, 86036Poitiers, France
André V.G. Cavalieri
Affiliation:
Divisão de Engenharia Aeronáutica, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP12228-900, Brazil
Rhiannon Kirby
Affiliation:
Laboratory for Turbulence Research in Aerospace and Combustion, Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC3800, Australia
Thales C.L. Fava
Affiliation:
Linné FLOW Centre, Department of Mechanics, KTH Royal Institute of Technology, SE-10044Stockholm, Sweden
Daniel Edgington-Mitchell
Affiliation:
Laboratory for Turbulence Research in Aerospace and Combustion, Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC3800, Australia
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We present a two-point model to investigate the underlying source mechanisms for broadband shock-associated noise (BBSAN) in shock-containing supersonic jets. In the model presented, the generation of BBSAN is assumed to arise from the nonlinear interaction between downstream-propagating coherent structures with the quasi-periodic shock cells in the jet plume. The turbulent perturbations are represented as axially extended wavepackets and the shock cells are modelled as a set of stationary waveguide modes. Unlike previous BBSAN models, the physical parameters describing the hydrodynamic components are not scaled using the acoustic field. Instead, the source characteristics of both the turbulent and shock components are extracted from the hydrodynamic region of large-eddy simulation and particle image velocimetry datasets. Apart from using extracted data, a reduced-order description of the wavepacket structure is obtained using parabolised stability equations. The validity of the model is tested by comparing far-field sound pressure level predictions to azimuthally decomposed experimental acoustic data from a cold Mach 1.5 underexpanded jet. At polar angles and frequencies where BBSAN dominates, encouraging comparisons of the radiated noise spectra for the first three azimuthal modes, in both frequency and amplitude (${\pm }2\ \textrm {dB}\,\textrm {St}^{-1}$ at peak frequency), reinforce the suitability of using reduced-order wavepacket sources for predicting BBSAN peaks. On the other hand, wavepacket jitter is found to have a critical role in recovering sound amplitude at interpeak frequencies. The paper presents a quantitative demonstration that the wavepacket–shock interaction, carefully reconstructed by extracting components from data or linearised models, contains the correct essential flow physics that accounts for most features of the far-field BBSAN spectra.

JFM classification

Acoustics: Aeroacoustics Acoustics: Jet noise
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 918 , 10 July 2021 , A9
Check for updates
Copyright
© 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.)

References

REFERENCES

André, B., Castelain, T. & Bailly, C. 2013 Broadband shock-associated noise in screeching and non-screeching underexpanded supersonic jets. AIAA J. 51 (3), 665–673.CrossRefGoogle Scholar
Ansaldi, T., Airiau, C., Pérez Arroyo, C. & Puigt, G. 2016 PSE-based sensitivity analysis of turbulent and supersonic single stream jet. In 22nd AIAA/CEAS Aeroacoustics Conference, p. 3052. AIAA.CrossRefGoogle Scholar
Antonialli, L.A., Cavalieri, A.V.G., Schmidt, O.T., Colonius, T., Jordan, P., Towne, A. & Brès, G.A. 2021 Amplitude scaling of wave packets in turbulent jets. AIAA J. 59 (2), 559–568.CrossRefGoogle Scholar
Arroyo, C.P. & Moreau, S. 2019 Azimuthal mode analysis of broadband shock-associated noise in an under-expanded axisymmetric jet. J. Sound Vib. 449, 64–83.CrossRefGoogle Scholar
Baqui, Y.B., Agarwal, A., Cavalieri, A.V.G. & Sinayoko, S. 2015 A coherence-matched linear source mechanism for subsonic jet noise. J. Fluid Mech. 776, 235–267.CrossRefGoogle Scholar
Beneddine, S., Mettot, C. & Sipp, D. 2015 Global stability analysis of underexpanded screeching jets. Eur. J. Mech. (B/Fluids) 49, 392–399.CrossRefGoogle Scholar
Bodony, D.J. & Lele, S.K. 2008 Low-frequency sound sources in high-speed turbulent jets. J. Fluid Mech. 617, 231–253.CrossRefGoogle Scholar
Bouthier, M. 1972 Stabilité linéaire des écoulements presque parallèles. J. Méc. 11, 599–621.Google Scholar
Brès, G.A., Ham, F.E., Nichols, J.W. & Lele, S.K. 2017 Unstructured large-eddy simulations of supersonic jets. AIAA J. 55 (4), 1164–1184.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, 83–124.CrossRefGoogle Scholar
Cavalieri, A.V.G. & Agarwal, A. 2014 Coherence decay and its impact on sound radiation by wavepackets. J. Fluid Mech. 748, 399–415.CrossRefGoogle Scholar
Cavalieri, A.V.G., Jordan, P., Agarwal, A. & Gervais, Y. 2011 Jittering wave-packet models for subsonic jet noise. J. Sound Vib. 330 (18–19), 4474–4492.CrossRefGoogle Scholar
Cavalieri, A.V.G., Jordan, P., Colonius, T. & Gervais, Y. 2012 Axisymmetric superdirectivity in subsonic jets. J. Fluid Mech. 704, 388–420.CrossRefGoogle Scholar
Cavalieri, A.V.G., Jordan, P. & Lesshafft, L. 2019 Wave-packet models for jet dynamics and sound radiation. Appl. Mech. Rev. 71 (2), 020802.CrossRefGoogle Scholar
Cavalieri, A.V.G., Rodríguez, D., Jordan, P., Colonius, T. & Gervais, Y. 2013 Wavepackets in the velocity field of turbulent jets. J. Fluid Mech. 730, 559–592.CrossRefGoogle Scholar
Crighton, D.G. & Gaster, M. 1976 Stability of slowly diverging jet flow. J. Fluid Mech. 77 (2), 397–413.CrossRefGoogle Scholar
Criminale, W.O., Jackson, T.L. & Joslin, R.D. 2018 Theory and Computation in Hydrodynamic Stability. Cambridge University Press.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), 118–188.CrossRefGoogle Scholar
Edgington-Mitchell, D., Honnery, D.R. & Soria, J. 2014 a The underexpanded jet Mach disk and its associated shear layer. Phys. Fluids 26 (9), 1578.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., Oberleithner, K., Honnery, D.R. & Soria, J. 2014 b Coherent structure and sound production in the helical mode of a screeching axisymmetric jet. J. Fluid Mech. 748, 822–847.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
Edgington-Mitchell, D.M., Duke, D., Harris, D., Wang, T., Schmidt, O.T., Jaunet, V., Jordan, P. & Towne, A. 2019 Modulation of downstream-propagating waves in jet screech. In AIAA/CEAS Aeroacoustics Conference 2019. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Fava, T.C. & Cavalieri, A.V. 2019 Propagation of acoustic waves in ducts with axially-varying parameters using the parabolized stability equations. In 25th AIAA/CEAS Aeroacoustics Conference, p. 2447. AIAA.CrossRefGoogle Scholar
Freund, J.B. 2001 Noise sources in a low-Reynolds-number turbulent jet at Mach 0.9. J. Fluid Mech. 438, 277–305.CrossRefGoogle Scholar
Freund, J.B. 2003 Noise-source turbulence statistics and the noise from a Mach 0.9 jet. Phys. Fluids 15 (6), 1788–1799.CrossRefGoogle Scholar
Gojon, R. & Bogey, C. 2017 Numerical study of the flow and the near acoustic fields of an underexpanded round free jet generating two screech tones. Intl J. Aeroacoust. 16 (7–8), 603–625.CrossRefGoogle Scholar
Goldstein, M.E. 1976 Aeroacoustics. New York.Google Scholar
Gudmundsson, K. & Colonius, T. 2011 Instability wave models for the near-field fluctuations of turbulent jets. J. Fluid Mech. 689, 97–128.CrossRefGoogle Scholar
Harper-Bourne, M. & Fisher, M.J. 1973 The noise from shock waves in supersonic jets. AGARD-CP-131 11, 1–13.Google Scholar
Herbert, T. 1997 Parabolized stability equations. Annu. Rev. Fluid Mech. 29 (1), 245–283.CrossRefGoogle Scholar
Hu, T.-F. & McLaughlin, D.K. 1990 Flow and acoustic properties of low Reynolds number underexpanded supersonic jets. J. Sound Vib. 141 (3), 485–505.CrossRefGoogle Scholar
Huber, J., Fleury, V., Bulté, J., Laurendeau, E. & Sylla, A.A. 2014 Understanding and reduction of cruise jet noise at aircraft level. Intl J. Aeroacoust. 13 (1–2), 61–84.CrossRefGoogle Scholar
Jordan, P. & Colonius, T. 2013 Wave packets and turbulent jet noise. Annu. Rev. Fluid Mech. 45, 173–195.CrossRefGoogle Scholar
Kalyan, A. & Karabasov, S.A. 2017 Broad band shock associated noise predictions in axisymmetric and asymmetric jets using an improved turbulence scale model. J. Sound Vib. 394, 392–417.CrossRefGoogle Scholar
Kaplan, O., Jordan, P., Cavalieri, A. & Brès, G.A. 2020 Nozzle dynamics and wavepackets in turbulent jets. arXiv:2007.00626.Google Scholar
Karabasov, S.A., Afsar, M.Z., Hynes, T.P., Dowling, A.P., McMullan, W.A., Pokora, C.D., Page, G.J. & McGuirk, J.J. 2010 Jet noise: acoustic analogy informed by large eddy simulation. AIAA J. 48 (7), 1312–1325.CrossRefGoogle Scholar
Kleine, V.G., Sasaki, K., Cavalieri, A.V., Brès, G.A. & Colonius, T. 2017 Evaluation of PSE as a model for supersonic jet using transfer functions. In 23rd AIAA/CEAS Aeroacoustics Conference, p. 4194. AIAA.CrossRefGoogle Scholar
Kopiev, V., Chernyshev, S., Zaitsev, M. & Kuznetsov, V. 2006 Experimental validation of instability wave theory for round supersonic jet. In 12th AIAA/CEAS Aeroacoustics Conference (27th AIAA Aeroacoustics Conference), p. 2595. AIAA.CrossRefGoogle Scholar
Kuo, C.-W., McLaughlin, D.K., Morris, P.J. & Viswanathan, K. 2015 Effects of jet temperature on broadband shock-associated noise. AIAA J. 53 (6), 1515–1530.CrossRefGoogle Scholar
Landahl, M.T., Mollo-Christensen, E. & Korman, M.S. 1989 Turbulence and random processes in fluid mechanics.CrossRefGoogle Scholar
Lele, S. 2005 Phased array models of shock-cell noise sources. In 11th AIAA/CEAS Aeroacoustics Conference, p. 2841. AIAA.CrossRefGoogle Scholar
Lessen, M., Fox, J.A. & Zien, H.M. 1965 The instability of inviscid jets and wakes in compressible fluid. J. Fluid Mech. 21 (1), 129–143.CrossRefGoogle Scholar
Lesshafft, L., Semeraro, O., Jaunet, V., Cavalieri, A.V.G. & Jordan, P. 2019 Resolvent-based modeling of coherent wave packets in a turbulent jet. Phys. Rev. Fluids 4 (6), 063901.CrossRefGoogle Scholar
Li, F. & Malik, M.R. 1997 Spectral analysis of parabolized stability equations. Comput. Fluids 26 (3), 279–297.CrossRefGoogle Scholar
Lighthill, M.J. 1952 On sound generated aerodynamically. I. General theory. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 211, pp. 564–587. The Royal Society.CrossRefGoogle Scholar
Maia, I.A., Jordan, P., Cavalieri, A.V.G. & Jaunet, V. 2019 Two-point wavepacket modelling of jet noise. Proc. R. Soc. A 475 (2227), 20190199.CrossRefGoogle ScholarPubMed
Markesteijn, A.P., Semiletov, V., Karabasov, S.A., Tan, D.J., Wong, M., Honnery, D. & Edgington-Mitchell, D.M. 2017 Supersonic jet noise: an investigation into noise generation mechanisms using large eddy simulation and high-resolution PIV data. In 23rd AIAA/CEAS Aeroacoustics Conference, p. 3029. AIAA.CrossRefGoogle Scholar
Martínez-Lera, P. & Schram, C. 2008 Correction techniques for the truncation of the source field in acoustic analogies. J. Acoust. Soc. Am. 124 (6), 3421–3429.CrossRefGoogle ScholarPubMed
Michalke, A. 1970 A wave model for sound generation in circular jets. Tech. Rep. Deutsche Forschungs-und Versuchsanstalt für Luft- und Raumfahrt.Google Scholar
Michalke, A. & Fuchs, H.V. 1975 On turbulence and noise of an axisymmetric shear flow. J. Fluid Mech. 70 (1), 179–205.CrossRefGoogle Scholar
Miller, S.A.E. & Morris, P.J. 2012 The prediction of broadband shock-associated noise including propagation effects. Intl J. Aeroacoust. 11 (7–8), 755–781.CrossRefGoogle Scholar
Mohseni, K. & Colonius, T. 2000 Numerical treatment of polar coordinate singularities. J. Comput. Phys. 157 (2), 787–795.CrossRefGoogle Scholar
Morris, P.J. & Miller, S.A.E. 2010 Prediction of broadband shock-associated noise using Reynolds-averaged Navier–Stokes computational fluid dynamics. AIAA J. 48 (12), 2931–2944.CrossRefGoogle Scholar
Norum, T. & Seiner, J. 1980 Location and propagation of shock associated noise from supersonic jets. In 6th Aeroacoustics Conference, p. 983. AIAA.CrossRefGoogle Scholar
Norum, T.D. & Seiner, J.M. 1982 Measurements of mean static pressure and far field acoustics of shock containing supersonic jets. Tech. Rep. NASA.Google Scholar
Obrist, D. & Kleiser, L. 2007 The influence of spatial domain truncation on the prediction of acoustic far-fields. In 13th AIAA/CEAS Aeroacoustics Conference (28th AIAA Aeroacoustics Conference), p. 3725. AIAA.CrossRefGoogle Scholar
O'Hara, D., Andersson, N., Jordan, P., Billson, M., Eriksson, L. & Davidson, L. 2004 A hybrid analysis methodology for improved accuracy in low-cost jet noise modelling. In 33rd International Congress and Exposition on Noise Control Engineering INTERNOISE 2004. Institute of Noise Control Engineering.Google Scholar
Pack, D.C. 1950 A note on prandtl's formula for the wave-length of a supersonic gas jet. Q. J. Mech. Appl. Maths 3 (2), 173–181.CrossRefGoogle Scholar
Panda, J. 1998 Shock oscillation in underexpanded screeching jets. J. Fluid Mech. 363, 173–198.CrossRefGoogle Scholar
Patel, T.K. & Miller, S.A.E. 2019 Statistical sources for broadband shock-associated noise using the Navier–Stokes equations. J. Acoust. Soc. Am. 146 (6), 4339–4351.CrossRefGoogle ScholarPubMed
Piantanida, S., Jaunet, V., Huber, J., Wolf, W.R., Jordan, P. & Cavalieri, A.V.G. 2016 Scattering of turbulent-jet wavepackets by a swept trailing edge. J. Acoust. Soc. Am. 140 (6), 4350–4359.CrossRefGoogle ScholarPubMed
Pickering, E.M., Towne, A., Jordan, P. & Colonius, T. 2020 Resolvent-based jet noise models: a projection approach. In AIAA Scitech 2020 Forum, p. 0999. AIAA.CrossRefGoogle Scholar
Powell, A. 1953 On the mechanism of choked jet noise. Proc. Phys. Soc. B 66 (12), 1039.CrossRefGoogle Scholar
Prandtl, L. 1904 Über die stationären Wellen in einem Gasstrahl. Hirzel.Google Scholar
Raman, G. 1999 Supersonic jet screech: half-century from powell to the present. J. Sound Vib. 225 (3), 543–571.CrossRefGoogle Scholar
Ray, P. & Lele, S.K. 2007 Sound generated by instability wave/shock-cell interaction in supersonic jets. J. Fluid Mech. 587, 173–215.CrossRefGoogle Scholar
Reba, R., Narayanan, S. & Colonius, T. 2010 Wave-packet models for large-scale mixing noise. Intl J. Aeroacoust. 9 (4–5), 533–557.CrossRefGoogle Scholar
Rodríguez, D., Cavalieri, A.V.G., Colonius, T. & Jordan, P. 2015 A study of linear wavepacket models for subsonic turbulent jets using local eigenmode decomposition of PIV data. Eur. J. Mech. (B/Fluids) 49, 308–321.CrossRefGoogle Scholar
Rodriguez, D., Sinha, A., Bres, G.A. & Colonius, T. 2013 Acoustic field associated with parabolized stability equation models in turbulent jets. In 19th AIAA/CEAS Aeroacoustics Conference, p. 2279. AIAA.CrossRefGoogle Scholar
Rodríguez, D., Sinha, A., Bres, G.A. & Colonius, T. 2013 Inlet conditions for wave packet models in turbulent jets based on eigenmode decomposition of large eddy simulation data. Phys. Fluids 25 (10), 105107.CrossRefGoogle Scholar
Saric, W.S. & Nayfeh, A.H. 1975 Nonparallel stability of boundary-layer flows. Phys. Fluids 18 (8), 945–950.CrossRefGoogle Scholar
Sasaki, K., Cavalieri, A.V.G., Jordan, P., Schmidt, O.T., Colonius, T. & Brès, G.A. 2017 a High-frequency wavepackets in turbulent jets. J. Fluid Mech. 830, R2.CrossRefGoogle Scholar
Sasaki, K., Piantanida, S., Cavalieri, A.V.G. & Jordan, P. 2017 b Real-time modelling of wavepackets in turbulent jets. J. Fluid Mech. 821, 458.CrossRefGoogle Scholar
Savarese, A., Jordan, P., Girard, S., Collin, E., Porta, M. & Gervais, Y. 2013 Experimental study of shock-cell noise in underexpanded supersonic jets. In 19th AIAA/CEAS Aeroacoustics Conference, p. 2080. AIAA.CrossRefGoogle Scholar
Schlinker, R., Simonich, J., Shannon, D., Reba, R., Colonius, T., Gudmundsson, K. & Ladeinde, F. 2009 Supersonic jet noise from round and chevron nozzles: experimental studies. In 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference), p. 3257. AIAA.CrossRefGoogle Scholar
Schmid, P.J., Henningson, D.S. & Jankowski, D.F. 2002 Stability and transition in shear flows. Applied mathematical sciences, vol. 142. Appl. Mech. Rev. 55 (3), B57–B59.CrossRefGoogle Scholar
Schmidt, O.T., 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, 1153–1181.CrossRefGoogle Scholar
Schmidt, O.T., Towne, A., Rigas, G., Colonius, T. & Brès, G.A. 2018 Spectral analysis of jet turbulence. J. Fluid Mech. 855, 953–982.CrossRefGoogle Scholar
Seiner, J.M. & Norum, T.D. 1980 Aerodynamic Aspects of Shock Containing Jet Plumes. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Seiner, J.M. & Yu, J.C. 1984 Acoustic near-field properties associated with broadband shock noise. AIAA J. 22 (9), 1207–1215.CrossRefGoogle Scholar
Shen, W., Patel, T.K. & Miller, S.A.E. 2021 A time domain approach for shock noise prediction with decomposition analyses of large-scale coherent turbulent structures in jets. J. Sound Vib. 499, 115996.CrossRefGoogle Scholar
Shur, M.L., Spalart, P.R. & Strelets, M.K. 2011 Noise prediction for underexpanded jets in static and flight conditions. AIAA J. 49 (9), 2000–2017.CrossRefGoogle Scholar
Sinha, A., Rodríguez, D., Brès, G.A. & Colonius, T. 2014 Wavepacket models for supersonic jet noise. J. Fluid Mech. 742, 71–95.CrossRefGoogle Scholar
Suzuki, T. 2016 Wave-packet representation of shock-cell noise for a single round jet. AIAA J. 54 (12), 3903–3917.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, 197–226.CrossRefGoogle Scholar
Tam, C.K.W. 1972 On the noise of a nearly ideally expanded supersonic jet. J. Fluid Mech. 51 (1), 69–95.CrossRefGoogle Scholar
Tam, C.K.W. 1987 Stochastic model theory of broadband shock associated noise from supersonic jets. J. Sound Vib. 116 (2), 265–302.CrossRefGoogle Scholar
Tam, C.K.W. 1990 Broadband shock-associated noise of moderately imperfectly expanded supersonic jets. J. Sound Vib. 140 (1), 55–71.CrossRefGoogle Scholar
Tam, C.K.W. 1995 Supersonic jet noise. Annu. Rev. Fluid Mech. 27 (1), 17–43.CrossRefGoogle Scholar
Tam, C.K.W. & Auriault, L. 1998 Mean flow refraction effects on sound radiated from localized sources in a jet. J. Fluid Mech. 370, 149–174.CrossRefGoogle Scholar
Tam, C.K.W. & Burton, D.E. 1984 Sound generated by instability waves of supersonic flows. Part 2. Axisymmetric jets. J. Fluid Mech. 138, 273–295.CrossRefGoogle Scholar
Tam, C.K.W. & Chen, K.C. 1979 A statistical model of turbulence in two-dimensional mixing layers. J. Fluid Mech. 92 (2), 303–326.CrossRefGoogle Scholar
Tam, C.K.W., Jackson, J.A. & Seiner, J.M. 1985 A multiple-scales model of the shock-cell structure of imperfectly expanded supersonic jets. J. Fluid Mech. 153, 123–149.CrossRefGoogle Scholar
Tam, C.K.W. & Tanna, H.K. 1982 Shock associated noise of supersonic jets from convergent-divergent nozzles. J. Sound Vib. 81 (3), 337–358.CrossRefGoogle Scholar
Tan, D.J., Edgington-Mitchell, D. & Honnery, D. 2015 Measurement of density in axisymmetric jets using a novel background-oriented schlieren (BOS) technique. Exp. Fluids 56 (11), 204.CrossRefGoogle Scholar
Tan, D.J., Honnery, D., Kalyan, A., Semiletov, V., Karabasov, S.A. & Edgington-Mitchell, D. 2018 Equivalent shock-associated noise source reconstruction of screeching underexpanded unheated round jets. AIAA J. 57 (3), 1200–1214.CrossRefGoogle Scholar
Tan, D.J., Honnery, D., Kalyan, A., Semiletov, V., Karabasov, S.A. & Edgington-Mitchell, D. 2019 Correlation analysis of high-resolution particle image velocimetry data of screeching jets. AIAA J. 57 (2), 735–748.CrossRefGoogle Scholar
Tan, D.J., Kalyan, A., Gryazev, V., Wong, M., Honnery, D., Edgington-Mitchell, D.M. & Karabasov, S.A. 2017 On the application of shock-associated noise models to PIV measurements of screeching axisymmetric cold jets. In 23rd AIAA/CEAS Aeroacoustics Conference, p. 3028. AIAA.CrossRefGoogle Scholar
Tissot, G., Lajús, F.C. jr, Cavalieri, A.V.G. & Jordan, P. 2017 a Wave packets and orr mechanism in turbulent jets. Phys. Rev. Fluids 2 (9), 093901.CrossRefGoogle Scholar
Tissot, G., Zhang, M., Lajús, F.C., Cavalieri, A.V.G. & Jordan, P. 2017 b Sensitivity of wavepackets in jets to nonlinear effects: the role of the critical layer. J. Fluid Mech. 811, 95–137.CrossRefGoogle Scholar
Towne, A., Schmidt, O.T. & Colonius, T. 2018 Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. J. Fluid Mech. 847, 821–867.CrossRefGoogle Scholar
Unnikrishnan, S., Cavalieri, A.V.G. & Gaitonde, D.V. 2019 Acoustically informed statistics for wave-packet models. AIAA J. 57 (6), 2421–2434.CrossRefGoogle Scholar
Uzun, A., Lyrintzis, A.S. & Blaisdell, G.A. 2004 Coupling of integral acoustics methods with LES for jet noise prediction. Intl J. Aeroacoust. 3 (4), 297–346.CrossRefGoogle Scholar
Vaughn, A.B., Neilsen, T.B., Gee, K.L., Wall, A.T., Micah Downing, J. & James, M.M. 2018 Broadband shock-associated noise from a high-performance military aircraft. J. Acoust. Soc. Am. 144 (3), EL242–EL247.CrossRefGoogle ScholarPubMed
Viswanathan, K. 2002 Aeroacoustics of hot jets. In 8th AIAA/CEAS Aeroacoustics Conference & Exhibit, p. 2481. AIAA.CrossRefGoogle Scholar
Viswanathan, K. 2006 Scaling laws and a method for identifying components of jet noise. AIAA J. 44 (10), 2274.CrossRefGoogle Scholar
Viswanathan, K., Alkislar, M.B. & Czech, M.J. 2010 Characteristics of the shock noise component of jet noise. AIAA J. 48 (1), 25–46.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, 421–448.CrossRefGoogle Scholar
Wishart, D.P. 1995 The structure of a heated supersonic jet operating at design and off-design conditions. PhD thesis. Florida State University.CrossRefGoogle Scholar
Wong, M.H., Edgington-Mitchell, D.M., Honnery, D., Cavalieri, A.V. & Jordan, P. 2019 a A parabolised stability equation based broadband shock-associated noise model. In 25th AIAA/CEAS Aeroacoustics Conference, p. 2584. AIAA.CrossRefGoogle Scholar
Wong, M.H., Jordan, P., Honnery, D.R. & Edgington-Mitchell, D. 2019 b Impact of coherence decay on wavepacket models for broadband shock-associated noise in supersonic jets. J. Fluid Mech. 863, 969–993.CrossRefGoogle Scholar
Wong, M.H., Kirby, R., Jordan, P. & Edgington-Mitchell, D. 2020 Azimuthal decomposition of the radiated noise from supersonic shock-containing jets. J. Acoust. Soc. Am. 148 (4), 2015–2027.CrossRefGoogle ScholarPubMed
Wu, X. 2005 Mach wave radiation of nonlinearly evolving supersonic instability modes in shear layers. J. Fluid Mech. 523, 121.CrossRefGoogle Scholar
Zhang, M., Jordan, P., Lehnasch, G., Cavalieri, A.V. & Agarwal, A. 2014 Just enough jitter for jet noise? In 20th AIAA/CEAS Aeroacoustics Conference, p. 3061. AIAA.CrossRefGoogle Scholar