Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-12-01T06:45:25.209Z Has data issue: false hasContentIssue false
  • English
  • Français

High-frequency wavepackets in turbulent jets

Published online by Cambridge University Press:  29 September 2017

Kenzo Sasaki Open the ORCID record for Kenzo Sasaki [Opens in a new window] ,
André V. G. Cavalieri ,
Peter Jordan ,
Oliver T. Schmidt Open the ORCID record for Oliver T. Schmidt [Opens in a new window] ,
Tim Colonius  and
Guillaume A. Brès Open the ORCID record for Guillaume A. Brès [Opens in a new window]
Kenzo Sasaki*
Affiliation:
Aerodynamics Department, Instituto Tecnológico de Aeronáutica, São José dos Campos 12228900, Brazil
André V. G. Cavalieri
Affiliation:
Aerodynamics Department, Instituto Tecnológico de Aeronáutica, São José dos Campos 12228900, Brazil
Peter Jordan
Affiliation:
Département Fluides, Thermique et Combustion, Institut Pprime, 86036 Poitiers, France
Oliver T. Schmidt
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
Tim Colonius
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
Guillaume A. Brès
Affiliation:
Cascade Technologies Inc., Palo Alto, CA 94303, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Wavepackets obtained as solutions of the flow equations linearised around the mean flow have been shown in recent work to yield good agreement, in terms of amplitude and phase, with those educed from turbulent jets. Compelling agreement has been demonstrated, for the axisymmetric and first helical mode, up to Strouhal numbers close to unity. We here extend the range of validity of wavepacket models to Strouhal number $St=4.0$ and azimuthal wavenumber $m=4$ by comparing solutions of the parabolised stability equations with a well-validated large-eddy simulation of a Mach 0.9 turbulent jet. The results show that the near-nozzle dynamics can be correctly described by the homogeneous linear model, the initial growth rates being accurately predicted for the entire range of frequencies and azimuthal wavenumbers considered. Similarly to the lower-frequency wavepackets reported prior to this work, the high-frequency linear waves deviate from the data downstream of their stabilisation locations, which move progressively upstream as the frequency increases.

JFM classification

Acoustics: Acoustics Acoustics: Aeroacoustics Acoustics: Jet noise
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 830 , 10 November 2017 , R2
Check for updates
Copyright
© 2017 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

Avital, E. J. & Sandham, N. D. 1997 A note on the structure of the acoustic field emitted by a wave packet. J. Sound Vib. 204 (3), 533–539.CrossRefGoogle Scholar
Beneddine, S., Sipp, D., Arnault, A., Dandois, J. & Lesshafft, L. 2016 Conditions for validity of mean flow stability analysis. J. Fluid Mech. 798, 485–504.CrossRefGoogle Scholar
Bowes, W. R., Bowler, D., Carnes, R., Fratarangelo, R., Rumpf, D., Heiser, W. H., Huff, D. L. & Moin, P.2009 Report on jet noise reduction. Tech. Rep., Naval Research Advisory Committee.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., Jaunet, V., Le Rallic, M., Jordan, P., Colonius, T. & Lele, S. K.2015 Large eddy simulation for jet noise: the importance of getting the boundary layer right. AIAA Paper 2015-2535.CrossRefGoogle Scholar
Brès, G. A., Jaunet, V., Le Rallic, M., Jordan, P., Towne, A., Schmidt, O. T., Colonius, T., Cavalieri, A. V. G. & Lele, S. K.2016 Large eddy simulation for jet noise: azimuthal decomposition and intermittency of the radiated sound. AIAA Paper 2016-3050.CrossRefGoogle Scholar
Brès, G. A., Jordan, P., Colonius, T., Le Rallic, M., Jaunet, V. & Lele, S. K. 2014 Large eddy simulation of a Mach 0.9 turbulent jet. In Proceedings of the Summer Program, Center for Turbulence Research, Stanford University.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.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
Chu, B.-T. 1965 On the energy transfer to small disturbances in fluid flow (Part I). Acta Mechanica 1 (3), 215–234.CrossRefGoogle Scholar
Crighton, D. G. & Gaster, M. 1976 Stability of slowly diverging jet flow. J. Fluid Mech. 77 (2), 387–413.CrossRefGoogle Scholar
Crighton, D. G. & Huerre, P. 1990 Shear layer pressure fluctuations and superdirective acoustic sources. J. Fluid Mech. 220, 355–368.CrossRefGoogle Scholar
Ffowcs Williams, J. E. & Hawkings, D. L. 1969 Sound generation by turbulence and surfaces in arbitrary motion. Phil. Trans. R. Soc. Lond. A 264, 321–342.Google Scholar
Fontaine, R. A., Elliott, G. S., Austin, J. M. & Freund, J. B. 2015 Very near-nozzle shear-layer turbulence and jet noise. J. Fluid Mech. 770, 27–51.CrossRefGoogle Scholar
Garnaud, X., Lesshafft, L., Schmid, P. J. & Huerre, P. 2013 The preferred mode of incompressible jets: linear frequency response analysis. J. Fluid Mech. 716, 189–202.CrossRefGoogle Scholar
Gloor, M., Obrist, D. & Kleiser, L. 2013 Linear stability and acoustic characteristics of compressible, viscous, subsonic coaxial jet flow. Phys. Fluids 25 (8), 084102.CrossRefGoogle 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. 2010 Jet noise measurements: past and present. Intl J. Aeroacoust. 9 (4), 559–588.CrossRefGoogle Scholar
Herbert, T. 1997 Parabolized stability equations. Annu. Rev. Fluid Mech. 29 (1), 245–283.CrossRefGoogle 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.CrossRefGoogle Scholar
Jeun, J., Nichols, J. W. & Jovanović, M. R. 2016 Input–output analysis of high-speed axisymmetric isothermal jet noise. Phys. Fluids 28 (4), 047101.CrossRefGoogle Scholar
Jordan, P. & Colonius, T. 2013 Wave packets and turbulent jet noise. Annu. Rev. Fluid Mech. 45, 173–195.CrossRefGoogle Scholar
Jordan, P., Zhang, M., Lehnasch, G. & Cavalieri, A. V. G.2017 Modal and non-modal linear wavepacket dynamics in turbulent jets. AIAA Paper 2017-3379.CrossRefGoogle Scholar
Koenig, M., Sasaki, K., Cavalieri, A. V. G., Jordan, P. & Gervais, Y. 2016 Jet-noise control by fluidic injection from a rotating plug: linear and nonlinear sound-source mechanisms. J. Fluid Mech. 788, 358–380.CrossRefGoogle Scholar
Lesshafft, L. & Huerre, P. 2007 Linear impulse response in hot round jets. Phys. Fluids 19 (2), 024102.CrossRefGoogle Scholar
Maia, I. A., Jordan, P., Jaunet, V. & Cavalieri, A. V. G.2017 Two-point wavepacket modelling of jet noise. AIAA Paper 2017-3380.CrossRefGoogle Scholar
Malik, M. R. & Chang, C.-L. 2000 Nonparallel and nonlinear stability of supersonic jet flow. Comput. Fluids 29 (3), 327–365.CrossRefGoogle Scholar
McKeon, B. J. & Sharma, A. S. 2010 A critical-layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336–382.CrossRefGoogle Scholar
Nichols, J. W. & Lele, S. K. 2011 Global modes and transient response of a cold supersonic jet. J. Fluid Mech. 669, 225–241.CrossRefGoogle Scholar
Obrist, D. 2009 Directivity of acoustic emissions from wave packets to the far field. J. Fluid Mech. 640, 165–186.CrossRefGoogle Scholar
Petersen, R. A. & Samet, M. M. 1988 On the preferred mode of jet instability. J. Fluid Mech. 194, 153–173.CrossRefGoogle 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.CrossRefGoogle Scholar
Sandham, N. D. & Salgado, A. M. 2008 Nonlinear interaction model of subsonic jet noise. Phil. Trans. R. Soc. Lond. A 366 (1876), 2745–2760.Google ScholarPubMed
Sasaki, K., Piantanida, S., Cavalieri, V. G. & Jordan, P. 2017 Real-time modelling of wavepackets in turbulent jets. J. Fluid Mech. 821, 458–481.CrossRefGoogle Scholar
Sasaki, K., Tissot, G., Cavalieri, A. V. G., Jordan, P. & Biau, D.2016 Closed-loop control of wavepackets in a free shear-layer. AIAA Paper 2016-2758.Google 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
Semeraro, O., Jaunet, V., Jordan, P., Cavalieri, A. V. & Lesshafft, L.2016 Stochastic and harmonic optimal forcing in subsonic jets. AIAA Paper 2016-2935.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
Tissot, G., Zhang, M., Lajús, F. C., Cavalieri, A. V. G. & Jordan, P. 2017 Sensitivity of wavepackets in jets to nonlinear effects: the role of the critical layer. J. Fluid Mech. 811, 95–137.CrossRefGoogle Scholar
Towne, A., Cavalieri, A. V. G., Jordan, P., Colonius, T., Schmidt, O., Jaunet, V. & Brès, G. A. 2017a Acoustic resonance in the potential core of subsonic jets. J. Fluid Mech. 825, 1113–1152.CrossRefGoogle Scholar
Towne, A., Colonius, T., Jordan, P., Cavalieri, A. V. G. & Brès, G. A.2015 Stochastic and nonlinear forcing of wavepackets in a Mach 0.9 jet. AIAA Paper 2015-2217.CrossRefGoogle Scholar
Towne, A., Schmidt, O. T. & Colonius, T.2017b Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. arXiv:1708.04393.CrossRefGoogle Scholar