Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-05-07T23:25:08.329Z Has data issue: false hasContentIssue false
  • English
  • Français

The effect of flight on a turbulent jet: coherent structure eduction and resolvent analysis

Published online by Cambridge University Press:  19 April 2024

Igor A. Maia Open the ORCID record for Igor A. Maia [Opens in a new window] ,
Liam Heidt Open the ORCID record for Liam Heidt [Opens in a new window] ,
Ethan Pickering Open the ORCID record for Ethan Pickering [Opens in a new window] ,
Tim Colonius Open the ORCID record for Tim Colonius [Opens in a new window] ,
Peter Jordan Open the ORCID record for Peter Jordan [Opens in a new window]  and
Guillaume A. Brès Open the ORCID record for Guillaume A. Brès [Opens in a new window]
Igor A. Maia*
Affiliation:
Divisão de Engenharia Aeronáutica, Instituto Tecnológico de Aeronáutica, São José dos Campos, 12228-900, Brazil
Liam Heidt
Affiliation:
Division of Mechanical and Civil Engineering, California Institute of Technology, Pasadena, CA 91101, USA
Ethan Pickering
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02138, USA
Tim Colonius
Affiliation:
Division of Mechanical and Civil Engineering, California Institute of Technology, Pasadena, CA 91101, USA
Peter Jordan
Affiliation:
Département Fluides, Thermique, Combustion, Institut Pprime, CNRS - Université de Poitiers - ENSMA, 86360 Chasseneuil-du-Poitou, France
Guillaume A. Brès
Affiliation:
Cascade R&D, Cadence Design Systems, San Jose, CA 95134, USA
*
†Email address for correspondence: igoriam@ita.br
Get access Rights & Permissions [Opens in a new window]

Abstract

We study coherent structures in subsonic turbulent jets subject to a flight stream. A thorough characterisation of the effects of a flight stream on the turbulent field was recently performed by Maia et al. (Phys. Rev. Fluids, vol. 8, 2023, 063902) and fluctuation energy attenuations were observed over a broad range of frequencies and azimuthal wavenumbers. The Kelvin–Helmholtz, Orr and lift-up mechanisms were all shown to be weakened by the flight stream. Here we expand upon that study and model the changes in the dynamics of jets in flight using global resolvent analysis. The resolvent model is found to correctly capture the main effects of the flight stream on the dynamics of coherent structures, which are educed from a large-eddy simulation database using spectral proper orthogonal decomposition. Three modifications of note are: the damping of low-frequency streaky/Orr structures that carry most of the fluctuation energy; a degradation of the low-rank behaviour of the jet in frequencies where modal instability mechanisms are dominant; and a rank decrease at very low Strouhal numbers. The latter effect is underpinned by larger gain separations predicted by the resolvent analysis, due to a reduction in the wavelength of associated flow structures. This leads to a clearer relative dominance of streaky structures generated by the lift-up mechanism, despite the fact that the lift-up mechanism has been weakened with respect to the static jet.

JFM classification

Acoustics: Jet noise Instability: Shear-flow instability Wakes/Jets: Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 985 , 25 April 2024 , A21
Check for updates
Copyright
© The Author(s), 2024. 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

Agüí, J.C. & Hesselink, L. 1988 Flow visualization and numerical analysis of a coflowing jet: a three-dimensional approach. J. Fluid Mech. 191, 19–45.CrossRefGoogle Scholar
Becker, H.A. & Massaro, T.A. 1968 Vortex evolution in a round jet. J. Fluid Mech. 31 (3), 435–448.CrossRefGoogle Scholar
Blanco, D.C.P., Martini, E., Sasaki, K. & Cavalieri, A.V.G. 2022 Improved convergence of the spectral proper orthogonal decomposition through time shifting. J. Fluid Mech. 950, A9.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.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
Browand, F.K. & Laufer, J. 1975 The roles of large scale structures in the initial development of circular jets. In Symposia on Turbulence in Liquids, University of Missouri-Rolla.Google Scholar
Bryce, W. 1984 The prediction of static-to-flight changes in jet noise. AIAA Paper 1984-2358.CrossRefGoogle Scholar
Bushel, K.W. 1975 Measurement and prediction of jet noise in flight. AIAA Paper 75-461.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, 4474–4492.CrossRefGoogle Scholar
Cavalieri, A.V.G., Jordan, P. & Lesshafft, L. 2019 Wave-packet models for jet dynamics and sound radiation. Appl. Mech. Rev. 71, 020802.CrossRefGoogle Scholar
Chu, B.-T. 1965 On the energy transfer to small scale disturbances in fluid flow (Part 1). Acta Mech. 1 (3), 215–234.CrossRefGoogle Scholar
Cocking, B.J. & Bryce, W.D. 1975 Subsonic jet noise in flight based on some wind tunnel results. AIAA Paper 75-462.CrossRefGoogle Scholar
Crighton, D.G., Ffowcs, J.E. & Cheeseman, I.C. 1977 The outlook for simulation of forward flight effects on aircraft noise. J. Aircraft 14 (11), 1117–1125.CrossRefGoogle 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.CrossRefGoogle Scholar
Dimotakis, P.E., Miake-Lye, R.C. & Papantoniou, D.A. 1983 Structure and dynamics of round turbulent jets. Phys. Fluids 26 (11), 3185–3192.CrossRefGoogle Scholar
Garnaud, X., Lesshafft, L., Schmid, P. & Huerre, P. 2013 The preferred mode of incompressible jets: linear frequency response analysis. J. Fluid Mech. 716, 189–202.CrossRefGoogle Scholar
Heidt, L., Colonius, T., Nekkanti, A., Schmdit, O., Maia, I. & Jordan, P. 2021 Analysis of forced subsonic jets using spectral proper orthogonal decomposition and resolvent analysis. AIAA Paper 2021-2108. AIAA Aviation 2021 Forum.CrossRefGoogle Scholar
Hwang, G.Y. & Cossu, C. 2010 Amplification of coherent streaks in the turbulent Couette flow: an input–output analysis at low Reynolds number. J. Fluid Mech. 633, 333–348.CrossRefGoogle Scholar
Jeun, J., Nichols, J.W. & Jovanovic, M.R. 2016 Input-output analysis of high-speed axisymmetric isothermal jet noise. Phys. Fluids (1994-present) 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. Modal and non-modal linear wavepacket dynamics in turbulent jets. AIAA Paper 2017-3379. 23rd AIAA/CEAS Aeroacoustics Conference. Available at: https://doi.org/10.2514/6.2017-3379.CrossRefGoogle Scholar
Jung, D., Gamard, S. & George, W.K. 2004 Downstream evolution of the most energetic modes in a turbulent axisymmetric jet at high Reynolds number. Part 1. The near-field region. J. Fluid Mech. 514, 173–204.CrossRefGoogle Scholar
Kaplan, O., Jordan, P., Cavalieri, A.V.G. & Brès, G. 2021 Nozzle dynamics and wavepackets in turbulent jets. J. Fluid Mech. 923, A22.CrossRefGoogle Scholar
Karban, U., Bugeat, B., Towne, A., Lesshafft, L., Agarwal, A. & Jordan, P. 2023 An empirical model of noise sources in subsonic jets. J. Fluid Mech. 965, A18.CrossRefGoogle Scholar
Karban, U., Martini, E., Jordan, P., Brès, G. & Towne, A. 2022 Solutions to aliasing in time-resolved flow data. Theor. Comput. Fluid Dyn. 36, 887–914.CrossRefGoogle Scholar
Kuhn, P., Soria, J. & Oberleithner, K. 2021 Linear modelling of self-similar jet turbulence. J. Fluid Mech. 919, A7.CrossRefGoogle Scholar
Lesshafft, L., Semeraro, O., Jaunet, V., Cavalieri, A.V.G. & Jordan, P. 2019 Resolvent based modelling of coherent structures wave packets in a turbulent jet. Phys. Rev. Fluids 4, 063901.CrossRefGoogle Scholar
Maia, I.A., Brès, G., Lesshafft, L. & Jordan, P. 2023 Effect of a flight stream on subsonic turbulent jets. Phys. Rev. Fluids 8, 063902.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, 20190199.CrossRefGoogle ScholarPubMed
Martinsson, P-G. 2019 Randomized methods for matrix computations. Math. Data 25 (4), 187–231.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.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
Michalke, A. & Hermann, G. 1982 On the inviscid instability of a circular jet with external flow. J. Fluid Mech. 114, 343–359.CrossRefGoogle Scholar
Mohseni, K. & Colonius, T. 2000 Numerical treatment of polar coordinate singularities. J. Comput. Phys. 157 (2), 787–795.CrossRefGoogle Scholar
Morfey, C.L. & Tester, B.J. 1977 Noise measurements in a free jet flight simulation facility: shear layer refraction and facility-to-flight corrections. J. Sound Vib. 54 (1), 83–106.CrossRefGoogle Scholar
Morra, P., Semeraro, O., Henningson, D.S. & Cossu, C. 2019 On the relevance of Reynolds stresses in resolvent analyses of turbulent wall-bounded flows. J. Fluid Mech. 867, 969–984.CrossRefGoogle Scholar
Nogueira, P., Cavalieri, A.V.G., Jordan, P. & Jaunet, V. 2019 Large-scale streaky structures in turbulent jets. J. Fluid Mech. 873, 211–237.CrossRefGoogle Scholar
Oberleithner, K., Paschereit, C.O. & Wygnanski, I. 2014 On the impact of swirl on the growth of coherent structures. J. Fluid Mech. 741, 156–199.CrossRefGoogle Scholar
Packman, A.B., Ng, K.W. & Paterson, R.W. 1975 Effect of simulated flight on subsonic jet exhaust noise. AIAA Paper 75-869.CrossRefGoogle Scholar
Pickering, E., Rigas, G., Nogueira, P., Cavalieri, A.V.G., Schmidt, O. & Colonius, T. 2020 Lift-up, Kelvin–Helmholtz and Orr mechanisms in turbulent jets. J. Fluid Mech. 896, A2.CrossRefGoogle Scholar
Pickering, E., Rigas, G., Schmidt, O.T., Sipp, D. & Colonius, T. 2021 Optimal eddy-viscosity models of coherent structures in turbulent jet. J. Fluid Mech. 917, A29.CrossRefGoogle Scholar
Plumbee, H.E. 1975 Effects of forward flight on turbulent jet mixing noise. AIAA Paper 75-869.Google Scholar
Rukes, L., Paschereit, O. & Oberleithner, K. 2016 An assessment of turbulence models for linear hydrodynamic stability analysis of strongly swirling jets. Eur. J. Fluid Mech. 59, 205–218.CrossRefGoogle Scholar
Sasaki, K., Cavalieri, A.V.G., Jordan, P., Schmidt, O.T., Colonius, T. & Brès, G. 2017 High-frequency wavepackets in turbulent jets. J. Fluid Mech. 830, R2.CrossRefGoogle Scholar
Schmidt, O.T., Towne, A., Colonius, T., Cavalieri, A.V.G., Jordan, P. & Brès, G. 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
Soares, L.F., Cavalieri, A.V.G., Kopiev, V. & Faranosov, G. 2020 Flight effects on turbulent-jet wave packets. AIAA J. 58 (9), 3877–3888.CrossRefGoogle Scholar
Tammisola, O. & Juniper, M.P. 2016 Coherent structures in a swirl injector at $Re = 4800$ by nonlinear simulations and linear global modes. J. Fluid Mech. 3 (5), 620–657.CrossRefGoogle Scholar
Tanna, H. & Morris, P. 1977 In-flight simulation experiments on turbulent jet mixing noise. J. Sound Vib. 53 (3), 343–359.CrossRefGoogle Scholar
Tissot, G., Zhang, M., Lajús, F.C. Jr., 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. 2017 Acoustic resonance in the potential core of subsonic jets. J. Fluid Mech. 825, 1113–1152.CrossRefGoogle Scholar
Towne, A., Lozano-Durán, A. & Yang, X. 2020 Resolvent-based estimation of space–time flow statistics. J. Fluid Mech. 883, A17.CrossRefGoogle Scholar
Tyacke, J.C., Wang, Z.-N. & Tucker, P.G. 2018 Noise source, length and time scale distributions in installed jets with a flight stream. AIAA Paper 2018-3619. 2018 AIAA/CEAS Aeroacoustics Conference, Atlanta, Georgia, USA.CrossRefGoogle Scholar
Viswanathan, K. & Czech, M. 2011 Measurement and modeling of effect of forward flight on jet noise. AIAA J. 49 (1), 216–234.CrossRefGoogle Scholar
Von Glahn, U., Groesbeck, D. & Goodykoontz, J. 1973 Velocity decay and acoustic characteristics of various nozzle geometries in forward flight. AIAA Paper 73-629.CrossRefGoogle Scholar
Wang, C., Lesshafft, L., Cavalieri, A.V.G. & Jordan, P. 2021 The effect of streaks on the instability of jets. J. Fluid Mech. 910, A14.CrossRefGoogle Scholar
Wang, Z-N., Naqavi, I. & Tucker, P.G. 2017 Large eddy simulation of the flight effects on single stream heated jets. AIAA Paper 2017-0457. 55th AIAA Aerospace Sciences Meeting, Grapevine, Texas, USA.CrossRefGoogle Scholar
Yule, A.J. 1978 Large-scale structure in the mixing layer of a round jet. J. Fluid Mech. 89 (3), 413–432.CrossRefGoogle Scholar