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Impact of coherence decay on wavepacket models for broadband shock-associated noise in supersonic jets

Published online by Cambridge University Press:  29 January 2019

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] ,
Damon R. Honnery Open the ORCID record for Damon R. Honnery [Opens in a new window]  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, VIC 3800, Australia
Peter Jordan
Affiliation:
Département Fluides, Thermique, Combustion, Institut Pprime, CNRS – Université de Poitiers – ENSMA, 86000 Poitiers, France
Damon R. Honnery
Affiliation:
Laboratory for Turbulence Research in Aerospace and Combustion, Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia
Daniel Edgington-Mitchell
Affiliation:
Laboratory for Turbulence Research in Aerospace and Combustion, Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia
*
†Email address for correspondence: [email protected]
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Abstract

Motivated by the success of wavepackets in modelling the noise from subsonic and perfectly expanded supersonic jets, we apply the wavepacket model to imperfectly expanded supersonic jets. Recent studies with subsonic jets have demonstrated the importance of capturing the ‘jitter’ of wavepackets in order to correctly predict the intensity of far-field sound. Wavepacket jitter may be statistically represented using a two-point coherence function; accurate prediction of noise requires identification of this coherence function. Following the analysis of Cavalieri & Agarwal (J. Fluid Mech., vol. 748, 2014. pp. 399–415), we extend their methodology to model the acoustic sources of broadband shock-associated noise in imperfectly expanded supersonic jets using cross-spectral densities of the turbulent and shock-cell quantities. The aim is to determine the relationship between wavepacket coherence-decay and far-field broadband shock-associated noise, using the model as a vehicle to explore the flow mechanisms at work. Unlike the subsonic case where inclusion of coherence decay amplifies the sound pressure level over the whole acoustic spectrum, we find that it does not play such a critical role in determining the peak sound amplitude for shock-cell noise. When higher-order shock-cell modes are used to reconstruct the acoustic spectrum at higher frequencies, however, the inclusion of a jittering wavepacket is necessary. These results suggest that the requirement for coherence decay identified in prior broadband shock-associated noise (BBSAN) models is in reality the statistical signature of jittering wavepackets. The results from this modelling approach suggest that nonlinear jittering effects of wavepackets need to be included in dynamic models for broadband shock-associated noise.

JFM classification

Instability: Absolute/convective instability Acoustics: Aeroacoustics Acoustics: Jet noise
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 863 , 25 March 2019 , pp. 969 - 993
Copyright
© 2019 Cambridge University Press 

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References

Antonialli, L. A., Cavalieri, A. V., Schmidt, O. T., Colonius, T., Jordan, P., Towne, A., Brés, G. & Agarwal, A. 2018 Amplitude scaling of turbulent-jet wavepackets. In 2018 AIAA/CEAS Aeroacoustics Conference, p. 2978. AIAA.Google Scholar
Baqui, Y. B., Agarwal, A., Cavalieri, A. V. G. & Sinayoko, S. 2013 Nonlinear and linear noise source mechanisms in subsonic jets. In 19th AIAA/CEAS Aeroacoustics Conference, p. 2087. AIAA.Google 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, 235–267.10.1017/jfm.2015.322Google Scholar
Breakey, D. E., Jordan, P., Cavalieri, A. V. G. & Léon, O. 2013 Near-field wavepackets and the far-field sound of a subsonic jet. In 19th AIAA/CEAS Aeroacoustics Conference, p. 2083. AIAA.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), 1164–1184.10.2514/1.J055084Google Scholar
Bridges, J. & Wernet, M. P. 2008 Turbulence associated with broadband shock noise in hot jets. In 14th AIAA/CEAS Aeroacoustics Conference, p. 2834. AIAA.Google Scholar
Cavalieri, A. V. G. & Agarwal, A. 2014 Coherence decay and its impact on sound radiation by wavepackets. J. Fluid Mech. 748, 399–415.10.1017/jfm.2014.186Google 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), 4474–4492.10.1016/j.jsv.2011.04.007Google Scholar
Cavalieri, A. V. G., Jordan, P., Colonius, T. & Gervais, Y. 2012 Axisymmetric superdirectivity in subsonic jets. J. Fluid Mech. 704, 388–420.10.1017/jfm.2012.247Google Scholar
Cavalieri, A. V. G., Jordan, P., Wolf, W. R. & Gervais, Y. 2014 Scattering of wavepackets by a flat plate in the vicinity of a turbulent jet. J. Sound Vib. 333 (24), 6516–6531.10.1016/j.jsv.2014.07.029Google 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, 559–592.10.1017/jfm.2013.346Google Scholar
Cheung, L. C. & Lele, S. K. 2009 Linear and nonlinear processes in two-dimensional mixing layer dynamics and sound radiation. J. Fluid Mech. 625, 321–351.10.1017/S0022112008005715Google Scholar
Crighton, D. G. 1975 Basic principles of aerodynamic noise generation. Prog. Aerosp. Sci. 16 (1), 31–96.10.1016/0376-0421(75)90010-XGoogle Scholar
Crow, S. Cj. & Champagne, F. H. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48 (3), 547–591.10.1017/S0022112071001745Google Scholar
Edgington-Mitchell, D., Oberleithner, K., Honnery, D. R. & Soria, J. 2014 Coherent structure and sound production in the helical mode of a screeching axisymmetric jet. J. Fluid Mech. 748, 822–847.10.1017/jfm.2014.173Google Scholar
Freund, J. B. 2003 Noise-source turbulence statistics and the noise from a mach 0.9 jet. Phys. Fluids 15 (6), 1788–1799.10.1063/1.1569919Google Scholar
Gudmundsson, K. & Colonius, T. 2011 Instability wave models for the near-field fluctuations of turbulent jets. J. Fluid Mech. 689, 97–128.10.1017/jfm.2011.401Google Scholar
Harper-Bourne, M. 2002 On modelling the near-field noise of the high-speed jet exhausts of combat aircraft. In 8th AIAA/CEAS Aeroacoustics Conference & Exhibit, p. 2424. AIAA.Google Scholar
Harper-Bourne, M. & Fisher, M. J. 1973 The noise from shock waves in supersonic jets. AGARD CP 11, 1–13.Google Scholar
Howe, M. S. 2003 Theory of Vortex Sound, vol. 33. Cambridge University Press.Google Scholar
Jaunet, V., Jordan, P. & Cavalieri, A. V. G. 2017 Two-point coherence of wave packets in turbulent jets. Phys. Rev. Fluids 2 (2), 024604.10.1103/PhysRevFluids.2.024604Google Scholar
Jordan, P. & Colonius, T. 2013 Wave packets and turbulent jet noise. Annu. Rev. Fluid Mech. 45, 173–195.10.1146/annurev-fluid-011212-140756Google Scholar
Jordan, P., Colonius, T., Bres, G. A., Zhang, M., Towne, A. & Lele, S. K. 2014 Modeling intermittent wavepackets and their radiated sound in a turbulent jet. In Proceedings of the Summer Program, p. 241. Center for Turbulence Research, Stanford University.Google Scholar
Jordan, P. & Gervais, Y. 2005 Modelling self- and shear-noise mechanisms in inhomogeneous, anisotropic turbulence. J. Sound Vib. 279 (3–5), 529–555.10.1016/j.jsv.2003.11.045Google 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, 392–417.10.1016/j.jsv.2017.01.027Google Scholar
Kerhervé, F., Fitzpatrick, J. & Jordan, P. 2006 The frequency dependence of jet turbulence for noise source modelling. J. Sound Vib. 296 (1–2), 209–225.10.1016/j.jsv.2006.02.012Google Scholar
Kerhervé, F., Jordan, P., Gervais, Y., Valiere, J. C. & Braud, P. 2004 Two-point laser doppler velocimetry measurements in a mach 1.2 cold supersonic jet for statistical aeroacoustic source model. Exp. Fluids 37 (3), 419–437.10.1007/s00348-004-0815-1Google Scholar
Landahl, M. T. & Mollo-Christensen, E. 1992 Turbulence and Random Processes in Fluid Mechanics. Cambridge University Press.10.1017/9781139174008Google Scholar
Lau, J. C. 1980 Laser velocimeter correlation measurements in subsonic and supersonic jets. J. Sound Vib. 70 (1), 85–101.10.1016/0022-460X(80)90556-8Google Scholar
Laufer, J. Y. T. C. 1983 Noise generation by a low-mach-number jet. J. Fluid Mech. 134, 1–31.10.1017/S0022112083003195Google Scholar
Lele, S. K. 2005 Phased array models of shock-cell noise sources. In 11th AIAA/CEAS Aeroacoustics Conference, p. 2841. AIAA.Google Scholar
Léon, O. & Brazier, J. P. 2013 Investigation of the near and far pressure fields of dual-stream jets using an Euler-based PSE model. In 19th AIAA/CEAS Aeroacoustics Conference, p. 2280. AIAA.Google Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically. I. General theory. Proc. R. Soc. Lond. A 211, 564–587.Google Scholar
Maia, I. A., Jordan, P., Jaunet, V. & Cavalieri, A. V. G. 2017 Two-point wavepacket modelling of jet noise. In 23rd AIAA/CEAS Aeroacoustics Conference, p. 3380. AIAA.Google Scholar
Michalke, A.1970 A wave model for sound generation in circular jets. Tech. Rep., Deutsche Luft- und Raumfahrt.Google Scholar
Miller, S. A. E. & Morris, P. J. 2010 The prediction of broadband shock-associated noise from dualstream and rectangular jets using RANS CFD. In 16th AIAA/CEAS Aeroacoustics Conference, p. 3730. AIAA.Google Scholar
Mollo-Christensen, E. 1967 Jet noise and shear flow instability seen from an experimenter’s viewpoint. J. Appl. Mech. 34 (1), 1–7.10.1115/1.3607624Google 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), 2931–2944.10.2514/1.J050560Google Scholar
Morris, P. J. & Zaman, K. B. M. Q. 2010 Velocity measurements in jets with application to noise source modeling. J. Sound Vib. 329 (4), 394–414.10.1016/j.jsv.2009.09.024Google Scholar
Norum, T. D. & Seiner, J. M.1982 Measurements of mean static pressure and far field acoustics of shock containing supersonic jets. Tech. Rep. TM 84521. NASA.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), 173–181.10.1093/qjmam/3.2.173Google Scholar
Pokora, C. D. & McGuirk, J. J. 2015 Stereo-PIV measurements of spatio-temporal turbulence correlations in an axisymmetric jet. J. Fluid Mech. 778, 216–252.10.1017/jfm.2015.362Google Scholar
Powell, A. 1953 On the mechanism of choked jet noise. Proc. Phys. Soc. B 66 (12), 1039.10.1088/0370-1301/66/12/306Google Scholar
Prandtl, L. 1904 Uber die stationären Wellen in einem Gasstrahl. Hirzel.Google Scholar
Ray, P. K. & Lele, S. K. 2007 Sound generated by instability wave/shock-cell interaction in supersonic jets. J. Fluid Mech. 587, 173–215.10.1017/S0022112007007306Google Scholar
Sandham, N. D., Morfey, C. L. & Hu, Z. W. 2006 Nonlinear mechanisms of sound generation in a perturbed parallel jet flow. J. Fluid Mech. 565, 1–23.10.1017/S0022112006001315Google Scholar
Sasaki, K., Cavalieri, A. V. G., Jordan, P., Schmidt, O. T., Colonius, T. & Brès, G. A. 2017a High-frequency wavepackets in turbulent jets. J. Fluid Mech. 830, R2.10.1017/jfm.2017.659Google Scholar
Sasaki, K., Piantanida, S., Cavalieri, A. V. G. & Jordan, P. 2017b Real-time modelling of wavepackets in turbulent jets. J. Fluid Mech. 821, 458–481.10.1017/jfm.2017.201Google Scholar
Savarese, A., Jordan, P., Girard, S., Royer, A., Fourment, C., Collin, E., Gervais, Y. & Porta, M. 2013 Experimental study of shock-cell noise in underexpanded supersonic jets. In 19th AIAA/CEAS Aeroacoustics Conference, p. 2080. AIAA.Google Scholar
Sinha, A., Rodríguez, D., Brès, G. A. & Colonius, T. 2014 Wavepacket models for supersonic jet noise. J. Fluid Mech. 742, 71–95.10.1017/jfm.2013.660Google Scholar
Suzuki, T. 2013 Coherent noise sources of a subsonic round jet investigated using hydrodynamic and acoustic phased-microphone arrays. J. Fluid Mech. 730, 659–698.10.1017/jfm.2013.337Google Scholar
Suzuki, T. 2016 Wave-packet representation of shock-cell noise for a single round jet. In 23rd AIAA/CEAS Aeroacoustics Conference, p. 4047. AIAA.Google 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, 197–226.10.1017/S0022112006001613Google Scholar
Tam, C. K. W. 1987 Stochastic model theory of broadband shock associated noise from supersonic jets. J. Sound Vib. 116 (2), 265–302.10.1016/S0022-460X(87)81303-2Google Scholar
Tam, C. K. W. 1990 Broadband shock-associated noise of moderately imperfectly expanded supersonic jets. J. Sound Vib. 140 (1), 55–71.10.1016/0022-460X(90)90906-GGoogle Scholar
Tam, C. K. W. 1995 Supersonic jet noise. Annu. Rev. Fluid Mech. 27 (1), 17–43.10.1146/annurev.fl.27.010195.000313Google 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, 123–149.10.1017/S0022112085001173Google Scholar
Tam, C. K. W., Seiner, J. M. & Yu, J. C. 1986 Proposed relationship between broadband shock associated noise and screech tones. J. Sound Vib. 110 (2), 309–321.10.1016/S0022-460X(86)80212-7Google Scholar
Tam, C. K. W. & Tanna, H. K. 1982 Shock associated noise of supersonic jets from convergent-divergent nozzles. J. Sound Vib. 81 (3), 337–358.10.1016/0022-460X(82)90244-9Google 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.Google Scholar
Towne, A., Colonius, T., Jordan, P., Cavalieri, A. V. G. & Bres, G. A. 2015 Stochastic and nonlinear forcing of wavepackets in a mach 0.9 jet. In 21st AIAA/CEAS Aeroacoustics Conference, p. 2217. AIAA.Google Scholar
Troutt, T. R. & Mclaughlin, D. K. 1982 Experiments on the flow and acoustic properties of a moderate-Reynolds-number supersonic jet. J. Fluid Mech. 116, 123–156.10.1017/S0022112082000408Google Scholar
Williams, J. E. F. & Kempton, A. J. 1978 The noise from the large-scale structure of a jet. J. Fluid Mech. 84 (4), 673–694.10.1017/S0022112078000415Google Scholar
Zhang, M. Q., Jordan, P., Lehnasch, G., Cavalieri, A. V. G. & Agarwal, A. 2014 Just enough jitter for jet noise? In 20th AIAA/CEAS Aeroacoustics Conference, p. 3061. AIAA.Google Scholar