Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-25T22:20:52.608Z Has data issue: false hasContentIssue false
  • English
  • Français

Wavepacket models for supersonic jet noise

Published online by Cambridge University Press:  21 February 2014

Aniruddha Sinha ,
Daniel Rodríguez ,
Guillaume A. Brès  and
Tim Colonius
Aniruddha Sinha*
Affiliation:
Engineering and Applied Sciences, California Institute of Technology, Pasadena, CA 91125, USA
Daniel Rodríguez
Affiliation:
School of Aeronautics, Universidad Politécnica de Madrid, E-28040 Madrid, Spain
Guillaume A. Brès
Affiliation:
Cascade Technologies Inc., Palo Alto, CA 94303, USA
Tim Colonius
Affiliation:
Engineering and Applied Sciences, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: sinha.aniruddha@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

Gudmundsson and Colonius (J. Fluid Mech., vol. 689, 2011, pp. 97–128) have recently shown that the average evolution of low-frequency, low-azimuthal modal large-scale structures in the near field of subsonic jets are remarkably well predicted as linear instability waves of the turbulent mean flow using parabolized stability equations. In this work, we extend this modelling technique to an isothermal and a moderately heated Mach 1.5 jet for which the mean flow fields are obtained from a high-fidelity large-eddy simulation database. The latter affords a rigourous and extensive validation of the model, which had only been pursued earlier with more limited experimental data. A filter based on proper orthogonal decomposition is applied to the data to extract the most energetic coherent components. These components display a distinct wavepacket character, and agree fairly well with the parabolized stability equations model predictions in terms of near-field pressure and flow velocity. We next apply a Kirchhoff surface acoustic propagation technique to the near-field pressure model and obtain an encouraging match for far-field noise levels in the peak aft direction. The results suggest that linear wavepackets in the turbulence are responsible for the loudest portion of the supersonic jet acoustic field.

JFM classification

Instability: Absolute/convective instability Acoustics: Aeroacoustics Acoustics: Jet noise
Type
Papers
Information
Journal of Fluid Mechanics , Volume 742 , 10 March 2014 , pp. 71 - 95
Copyright
© 2014 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

Alkislar, M. B., Krothapalli, A. & Butler, G. W. 2007 The effect of streamwise vortices on the aeroacoustics of a Mach 0.9 jet. J. Fluid Mech. 578, 139–169.CrossRefGoogle Scholar
Balakumar, P. 1998 Prediction of supersonic jet noises. In 36th AIAA Aerospace Sciences Meeting, AIAA Paper 1998–1057.Google Scholar
Baqui, Y., Agarwal, A., Cavalieri, A. V. G. & Sinayoko, S. 2013 Nonlinear and linear noise source mechanisms in subsonic jets. In 19th AIAA/CEAS Aeroacoustics Conference, AIAA Paper 2013–2087.Google 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, 352–385.Google Scholar
Breakey, D. E. S., Jordan, P., Cavalieri, A. V. G., Léon, O., Zhang, M., Lehnasch, G., Colonius, T. & Rodríguez, D. 2013 Near-field wavepackets and the far-field sound of a subsonic jet. In 19th AIAA/CEAS Aeroacoustics Conference, AIAA Paper 2013–2083.Google Scholar
Brès, G. A., Nichols, J. W., Lele, S. K. & Ham, F. E. 2012 Towards best practices for jet noise predictions with unstructured large eddy simulations. In 42nd AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2012–2965.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64 (4), 775–816.Google 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., 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
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.Google Scholar
Crighton, D. G. & Gaster, M. 1976 Stability of slowly diverging jet flow. J. Fluid Mech. 77 (2), 397–413.Google Scholar
Crow, S. & Champagne, F. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48 (3), 547–591.Google Scholar
Day, M. J., Mansour, N. N. & Reynolds, W. C. 2001 Nonlinear stability and structure of compressible reacting mixing layers. J. Fluid Mech. 446, 375–408.Google Scholar
Freund, J. B. 1997 Compressibility effects in a turbulent axisymmetric mixing layer. PhD thesis, Stanford University.Google Scholar
Freund, J. B. 2001 Noise sources in a low-Reynolds-number turbulent jet at Mach 0.9. J. Fluid Mech. 438 (1), 277–305.Google Scholar
Freund, J. B. & Colonius, T. 2009 Turbulence and sound-field POD analysis of a turbulent jet. Intl J. Aeroacoust. 8 (4), 337–354.CrossRefGoogle Scholar
Goldstein, M. E. & Leib, S. J. 2005 The role of instability waves in predicting jet noise. J. Fluid Mech. 525, 37–72.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
Henderson, B. 2010 Fifty years of fluidic injection for jet noise reduction. Intl J. Aeroacoust. 9 (1–2), 91–122.Google Scholar
Herbert, T. 1997 Parabolized stability equations. Annu. Rev. Fluid Mech. 29, 245–283.Google Scholar
Iollo, A., Lanteri, S. & Desideri, J.-A. 2000 Stability properties of POD-Galerkin approximations for the compressible Navier–Stokes equations. Theor. Comput. Fluid Dyn. 13 (6), 377–396.CrossRefGoogle Scholar
Jordan, P. & Colonius, T. 2013 Wave packets and turbulent jet noise. Annu. Rev. Fluid Mech. 45, 173–195.Google Scholar
Kerhervé, F., Jordan, P., Cavalieri, A. V. G., Delville, J., Bogey, C. & Juvé, D. 2012 Educing the source mechanism associated with downstream radiation in subsonic jets. J. Fluid Mech. 710, 606–640.Google 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. Proc. R. Soc. Lond.A 211 (1107), 564–587.Google Scholar
Lin, R.-S., Reba, R., Narayanan, S., Hariharan, N. S. & Bertolotti, F. P. 2004 Parabolized stability equation based analysis of noise from an axisymmetric hot jet. In Proceedings of ASME FEDSM, HT-FED2004-56820.Google Scholar
Malkus, W. V. R. 1956 Outline of a theory of turbulent shear flow. J. Fluid Mech. 1 (5), 521–539.CrossRefGoogle Scholar
Mankbadi, R. & Liu, J. T. C. 1984 Sound generated aerodynamically revisited: large-scale structures in a turbulent jet as a source of sound. Proc. R. Soc. Lond. A 311 (1516), 183–217.Google Scholar
Mattingly, G. E. & Chang, C. C. 1974 Unstable waves on an axisymmetric jet column. J. Fluid Mech. 65 (3), 541–560.CrossRefGoogle Scholar
Michalke, A. 1984 Survey on jet instability theory. Prog. Aerosp. Sci. 21, 159–199.Google Scholar
Mohseni, K. & Colonius, T. 2000 Numerical treatment of polar coordinate singularities. J. Comput. Phys. 157, 787–795.Google Scholar
Mohseni, K., Colonius, T. & Freund, J. B. 2002 An evaluation of linear instability waves as sources of sound in a supersonic turbulent jet. Phys. Fluids 14 (10), 3593–3600.Google Scholar
Mollo-Christensen, E. 1963 Measurements of near field pressure of subsonic jets. Tech. Rep. NATO A.G.A.R.D. Report 449.Google Scholar
Mollo-Christensen, E. 1967 Jet noise and shear flow instability seen from an experimenter’s point of view. J. Appl. Mech. 34 (1), 1–7.Google Scholar
Morse, P. M. & Ingard, K. 1968 Theoretical Acoustics. McGraw-Hill.Google Scholar
Piot, E., Casalis, G., Muller, F. & Bailly, C. 2006 Investigation of the PSE approach for subsonic and supersonic hot jets. Detailed comparisons with LES and linearized Euler equations results. Intl J. Aeroacoust. 5 (4), 361–393.Google Scholar
Reba, R., Narayanan, S. & Colonius, T. 2010 Wave-packet models for large-scale mixing noise. Intl J. Aeroacoust. 9 (4–5), 533–558.Google Scholar
Rodríguez, D., Sinha, A., Brès, G. & Colonius, T. 2013 Inlet conditions for wave packet models in turbulent jets based on eigenmode decomposition of large eddy simulation data. Phys. Fluids 25, 105107.CrossRefGoogle Scholar
Samimy, M., Kim, J.-H., Kearney-Fischer, M. & Sinha, A. 2012 High-speed and high Reynolds number jet control using localized arc filament plasma actuators. J. Propul. Power 28 (2), 269–280.Google Scholar
Schlinker, R. H., Simonich, J. C., Shannon, D. W., Reba, R., Colonius, T., Gudmundsson, K. & Ladiende, F. 2009 Supersonic jet noise from round and chevron nozzles: experimental studies. In 15th AIAA/CEAS Aeroacoustics Conference, AIAA Paper 2009–3257.Google Scholar
Shur, M. L., Spalart, P. R. & Strelets, M. K. 2005 Noise prediction for increasingly complex jets. Part I: methods and tests. Intl J. Aeroacoust. 4 (3–4), 213–246.Google Scholar
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures, Parts I–III. Q. Appl. Maths XLV (3), 561–590.Google Scholar
Suponitsky, V., Sandham, N. D. & Morfey, C. L. 2010 Linear and nonlinear mechanisms of sound radiation by instability waves in subsonic jets. J. Fluid Mech. 658, 509–538.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.Google Scholar
Tam, C. K. W. 1971 Directional acoustic radiation from a supersonic jet generated by shear layer instability. J. Fluid Mech. 46 (4), 757–768.Google Scholar
Tam, C. K. W. 1991 Jet noise generated by large-scale coherent motion. In Aeroacoustics of flight vehicles: Theory and practice. Volume 1: Noise sources (ed. Hubbard, H. H.), pp. 311–390. NASA RP-1258.Google Scholar
Tam, C. K. W. 1995 Supersonic jet noise. Annu. Rev. Fluid Mech. 27 (1), 17–43.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.Google Scholar
Tam, C. K. W. & Chen, P. 1994 Turbulent mixing noise from supersonic jets. AIAA J. 32 (9), 1774–1780.Google Scholar
Tam, C. K. W. & Hu, F. Q. 1989 On the three families of instability waves of high-speed jets. J. Fluid Mech. 201, 447–483.CrossRefGoogle Scholar
Tam, C. K. W. & Morris, P. J. 1985 Tone excited jets, Part V: a theoretical model and comparison with experiment. J. Sound Vib. 102, 119–151.CrossRefGoogle Scholar
Thompson, K. W. 1987 Time dependent boundary conditions for hyperbolic systems. J. Comput. Phys. 68, 1–24.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.CrossRefGoogle Scholar
Vreman, A. W. 2004 An eddy-viscosity subgrid-scale model for turbulent shear flow: algebraic theory and applications. Phys. Fluids 16 (10), 3670–3681.Google Scholar
Yen, C. C. & Messersmith, N. L. 1998 Application of parabolized stability equations to the prediction of jet instabilities. AIAA J. 36 (8), 1541–1544.CrossRefGoogle Scholar
Yen, C. C. & Messersmith, N. L. 1999 The use of compressible parabolized stability equations for prediction of jet instabilities and noise. In 5th AIAA/CEAS Aeroacoustics Conference, AIAA Paper 1999–1859.Google Scholar
You, D. & Moin, P. 2007 A dynamic global-coefficient subgrid-scale eddy-viscosity model for large-eddy simulation in complex geometries. Phys. Fluids 19, 065110.Google Scholar
Zaman, K. B. M. Q. 2012 Effect of initial boundary-layer state on subsonic jet noise. AIAA J. 50 (8), 1784–1795.Google Scholar