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Wavepackets and trapped acoustic modes in a turbulent jet: coherent structure eduction and global stability

Published online by Cambridge University Press:  27 July 2017

Oliver T. Schmidt Open the ORCID record for Oliver T. Schmidt [Opens in a new window] ,
Aaron Towne Open the ORCID record for Aaron Towne [Opens in a new window] ,
Tim Colonius ,
André V. G. Cavalieri ,
Peter Jordan  and
Guillaume A. Brès
Oliver T. Schmidt*
Affiliation:
California Institute of Technology, Pasadena, CA 91125, USA
Aaron Towne
Affiliation:
California Institute of Technology, Pasadena, CA 91125, USA Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA
Tim Colonius
Affiliation:
California Institute of Technology, Pasadena, CA 91125, USA
André V. G. Cavalieri
Affiliation:
Instituto Tecnológico de Aeronáutica, São José dos Campos, Brazil
Peter Jordan
Affiliation:
Institut Pprime, CNRS – University of Poitiers – ENSMA, Poitiers, France
Guillaume A. Brès
Affiliation:
Cascade Technologies, Inc., Palo Alto, CA 94303, USA
*
†Email address for correspondence: [email protected]
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Abstract

Coherent features of a turbulent Mach 0.9, Reynolds number $10^{6}$ jet are educed from a high-fidelity large eddy simulation. Besides the well-known Kelvin–Helmholtz instabilities of the shear layer, a new class of trapped acoustic waves is identified in the potential core. A global linear stability analysis based on the turbulent mean flow is conducted. The trapped acoustic waves form branches of discrete eigenvalues in the global spectrum, and the corresponding global modes accurately match the educed structures. Discrete trapped acoustic modes occur in a hierarchy determined by their radial and axial order. A local dispersion relation is constructed from the global modes and found to agree favourably with an empirical dispersion relation educed from the simulation data. The product between direct and adjoint modes is then used to isolate the trapped waves. Under certain conditions, resonance in the form of a beating occurs between trapped acoustic waves of positive and negative group velocities. This resonance explains why the trapped modes are prominently observed in the simulation and as tones in previous experimental studies. In the past, these tones were attributed to external factors. Here, we show that they are an intrinsic feature of high-subsonic jets that can be unambiguously identified by a global linear stability analysis.

JFM classification

Instability: Absolute/convective instability Acoustics: Aeroacoustics Acoustics: Jet noise
Type
Papers
Information
Journal of Fluid Mechanics , Volume 825 , 25 August 2017 , pp. 1153 - 1181
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Copyright
© 2017 Cambridge University Press 

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References

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.Google Scholar
Bodony, D. J. & Lele, S. K. 2008 Current status of jet noise predictions using large-eddy simulation. AIAA J. 46 (2), 364–380.CrossRefGoogle 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.Google 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 2015-3535.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. In 22nd AIAA/CEAS Aeroacoustics Conference, American Institute of Aeronautics and Astronautics (AIAA).Google 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 Center for Turbulence Research Proceedings of the Summer Program, p. 221.Google Scholar
Briggs, R. J. 1964 Electron-stream Interaction with Plasmas. MIT Press.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.Google Scholar
Chandler, G. J., Juniper, M. P., Nichols, J. W. & Schmid, P. J. 2012 Adjoint algorithms for the Navier–Stokes equations in the low mach number limit. J. Comput. Phys. 231 (4), 1900–1916.CrossRefGoogle Scholar
Chomaz, J.-M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357–392.Google Scholar
Chu, B.-T. 1965 On the energy transfer to small disturbances in fluid flow (Part I). Acta Mechanica 1 (3), 215–234.Google Scholar
Crighton, D. G. & Gaster, M. 1976 Stability of slowly diverging jet flow. J. Fluid Mech. 77 (02), 397–413.Google Scholar
Crouch, J. D., Garbaruk, A. & Magidov, D. 2007 Predicting the onset of flow unsteadiness based on global instability. J. Comput. Phys. 224 (2), 924–940.Google Scholar
Crow, S. C. & Champagne, F. H. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48 (03), 547–591.CrossRefGoogle Scholar
Farrell, B. F. & Ioannou, P. J. 1993 Stochastic forcing of the linearized Navier–Stokes equations. Phys. Fluids A 5 (11), 2600–2609.Google Scholar
Garnaud, X., Lesshafft, L., Schmid, P. J. & Huerre, P. 2013a Modal and transient dynamics of jet flows. Phys. Fluids 25 (4), 044103.Google Scholar
Garnaud, X., Lesshafft, L., Schmid, P. J. & Huerre, P. 2013b The preferred mode of incompressible jets: linear frequency response analysis. J. Fluid Mech. 716, 189–202.Google Scholar
Giannetti, F. & Luchini, P. 2007 Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech. 581, 167–197.CrossRefGoogle Scholar
Gudmundsson, K. & Colonius, T. 2011 Instability wave models for the near-field fluctuations of turbulent jets. J. Fluid Mech. 689, 97–128.Google Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22 (1), 473–537.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.Google Scholar
Jordan, P. & Colonius, T. 2013 Wave packets and turbulent jet noise. Annu. Rev. Fluid Mech. 45, 173–195.CrossRefGoogle Scholar
Mattsson, K. & Nordström, J. 2004 Summation by parts operators for finite difference approximations of second derivatives. J. Comput. Phys. 199 (2), 503–540.Google Scholar
McKeon, B. J. & Sharma, A. S. 2010 A critical-layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336–382.CrossRefGoogle Scholar
Meliga, P., Pujals, G. & Serre, É. 2012 Sensitivity of 2-d turbulent flow past a d-shaped cylinder using global stability. Phys. Fluids 24 (6), 061701.Google Scholar
Mettot, C., Sipp, D. & Bézard, H. 2014 Quasi-laminar stability and sensitivity analyses for turbulent flows: prediction of low-frequency unsteadiness and passive control. Phys. Fluids 26 (4), 045112.CrossRefGoogle Scholar
Michalke, A. 1971 Instability of a compressible circular free jet with consideration of the influence of the jet boundary layer thickness. Z. Flugwiss. 19 (8), 319–328.Google Scholar
Michalke, A. 1984 Survey on jet instability theory. Prog. Aerosp. Sci. 21, 159–199.CrossRefGoogle Scholar
Mohseni, K. & Colonius, T. 2000 Numerical treatment of polar coordinate singularities. J. Comput. Phys. 157 (2), 787–795.Google Scholar
Mollo-Christensen, E.1963 Measurements of near field pressure of subsonic jets. Tech. Rep. Advis. Group Aeronaut. Res. Dev.Google Scholar
Nichols, J. W. & Lele, S. K. 2011 Global modes and transient response of a cold supersonic jet. J. Fluid Mech. 669, 225–241.Google Scholar
Qadri, U. A. & Schmid, P. J. 2017 Effect of nonlinearities on the frequency response of a round jet. Phys. Rev. Fluids 2, 043902.Google Scholar
Semeraro, O., Lesshafft, L., Jaunet, V. & Jordan, P. 2016 Modeling of coherent structures in a turbulent jet as global linear instability wavepackets: theory and experiment. Intl J. Heat Fluid Flow 62, 24–32.Google Scholar
Sipp, D., Marquet, O., Meliga, P. & Barbagallo, A. 2010 Dynamics and control of global instabilities in open-flows: a linearized approach. Appl. Mech. Rev. 63 (3), 030801.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 (1), 197–226.CrossRefGoogle Scholar
Tam, C. K. W. & Ahuja, K. K. 1990 Theoretical model of discrete tone generation by impinging jets. J. Fluid Mech. 214, 67–87.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.Google 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.Google Scholar
Towne, A., Cavalieri, A. V. G., Jordan, P., Colonius, T., Schmidt, O. T., Jaunet, V. & Brès, G. A. 2017 Acoustic resonance in the potential core of subsonic jets. J. Fluid Mech. 825, 1113–1152.Google 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. In 21st AIAA/CEAS Aeroacoustics Conference, p. 2217.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