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Investigation of supersonic twin-jet coupling using spatial linear stability analysis

Published online by Cambridge University Press:  14 May 2021

Petrônio A.S. Nogueira Open the ORCID record for Petrônio A.S. Nogueira [Opens in a new window]  and
Daniel M. Edgington-Mitchell Open the ORCID record for Daniel M. Edgington-Mitchell [Opens in a new window]
Petrônio A.S. Nogueira*
Affiliation:
Department of Mechanical and Aerospace Engineering, Laboratory for Turbulence Research in Aerospace and Combustion, Monash University, Clayton3800, Australia
Daniel M. Edgington-Mitchell
Affiliation:
Department of Mechanical and Aerospace Engineering, Laboratory for Turbulence Research in Aerospace and Combustion, Monash University, Clayton3800, Australia
*
†Email address for correspondence: petronio.augusto@gmail.com
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Abstract

The present work focuses on the study of the resonance and coupling of an underexpanded circular twin-jet system operating at a nozzle pressure ratio of $5.0$. Particle image velocimetry data from previous work were revisited, and a symmetry-imposed proper orthogonal decomposition (POD) was performed. It is shown that the system is dominated by a single POD mode pair symmetric about the internozzle plane, and the resonance loop is modulated by a third POD mode related to shear thickness modulation. A spatial Fourier transform of the leading POD mode pair leads to the identification of the peak wavenumbers and radial shapes of the different waves at play in the screech phenomenon. Locally parallel linear stability analysis around the experimental mean flow is also performed, in order to provide clarification of the mode ‘locking’ mechanism, i.e. the selection of the global mode associated with screech. It is shown that the characteristics of the Kelvin–Helmholtz wavepackets alone are not sufficient to explain the coupling observed in the experimental data. A consideration of the upstream-travelling guided jet mode offers an explanation; only specific symmetries of upstream modes can be supported in the frequency range at which resonance occurs. Results from stability analysis point to structures at frequencies and wavenumbers close to those found experimentally, and their spatial structures show excellent agreement with the POD modes. The present results suggest that the resonance loop is closed by an upstream-travelling guided jet mode for the twin-jet system at high nozzle pressure ratio.

JFM classification

Acoustics: Aeroacoustics Acoustics: Jet noise Instability: Shear-flow instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 918 , 10 July 2021 , A38
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Alkislar, M.B., Krothapalli, A., Choutapalli, I. & Lourenco, L. 2005 Structure of supersonic twin jets. AIAA J. 43 (11), 2309–2318.CrossRefGoogle 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.CrossRefGoogle Scholar
Bayliss, A. & Turkel, E. 1992 Mappings and accuracy for Chebyshev pseudo-spectral approximations. J. Comput. Phys. 101 (2), 349–359.CrossRefGoogle Scholar
Bell, G., Cluts, J., Samimy, M., Soria, J. & Edgington-Mitchell, D. 2021 Intermittent modal coupling in screeching underexpanded circular twin jets. J. Fluid Mech. 910, A20.CrossRefGoogle Scholar
Bell, G., Soria, J., Honnery, D. & Edgington-Mitchell, D. 2017 Particle image velocimetry analysis of the twin supersonic jet structure and standing-wave. In 23rd AIAA/CEAS Aeroacoustics Conference, p. 3517. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Bell, G., Soria, J., Honnery, D. & Edgington-Mitchell, D. 2018 An experimental investigation of coupled underexpanded supersonic twin-jets. Exp. Fluids 59 (9), 139.CrossRefGoogle Scholar
Berkooz, G., Holmes, P. & Lumley, J.L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25 (1), 539–575.CrossRefGoogle Scholar
Cavalieri, A.V.G., Jordan, P., Colonius, T. & Gervais, Y. 2012 Axisymmetric superdirectivity in subsonic jets. J. Fluid Mech. 704, 388–420.CrossRefGoogle Scholar
Cavalieri, A.V.G., Jordan, P. & Lesshafft, L. 2019 Wave-packet models for jet dynamics and sound radiation. Appl. Mech. Rev. 71 (2), 020802.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
Crighton, D.G. 1975 Basic principles of aerodynamic noise generation. Prog. Aerosp. Sci. 16 (1), 31–96.CrossRefGoogle Scholar
Crow, S.C. & Champagne, F.H. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48 (3), 547–591.CrossRefGoogle Scholar
Davies, M.G. & Oldfield, D.E.S. 1962 Tones from a choked axisymmetric jet. I. Cell structure, eddy velocity and source locations. Acta Acust. 12 (4), 257–267.Google Scholar
Edgington-Mitchell, D. 2019 Aeroacoustic resonance and self-excitation in screeching and impinging supersonic jets – a review. Intl J. Aeroacoust. 18 (2–3), 118–188.CrossRefGoogle Scholar
Edgington-Mitchell, D., Honnery, D.R. & Soria, J. 2014 a The underexpanded jet mach disk and its associated shear layer. Phys. Fluids 26 (9), 096101.CrossRefGoogle Scholar
Edgington-Mitchell, D., Jaunet, V., Jordan, P., Towne, A., Soria, J. & Honnery, D. 2018 Upstream-travelling acoustic jet modes as a closure mechanism for screech. J. Fluid Mech. 855, R1.CrossRefGoogle Scholar
Edgington-Mitchell, D., Oberleithner, K., Honnery, D.R. & Soria, J. 2014 b Coherent structure and sound production in the helical mode of a screeching axisymmetric jet. J. Fluid Mech. 748, 822–847.CrossRefGoogle Scholar
Edgington-Mitchell, D., Wang, T., Nogueira, P., Schmidt, O., Jaunet, V., Duke, D., Jordan, P. & Towne, A. 2021 Waves in screeching jets. J. Fluid Mech. 913, A7.CrossRefGoogle Scholar
Gojon, R., Bogey, C. & Mihaescu, M. 2018 Oscillation modes in screeching jets. AIAA J. 56 (7), 2918–2924.CrossRefGoogle Scholar
Gudmundsson, K. 2009 Instability wave models of turbulent jets from round and serrated nozzles. PhD thesis, California Institute of Technology.Google Scholar
Harper-Bourne, M. & Fisher, M.J. 1974 The noise from shock waves in supersonic jets. AGARD CP-131 11, 1–13.Google Scholar
Jaunet, V, Collin, E & Delville, J 2016 POD-Galerkin advection model for convective flow: application to a flapping rectangular supersonic jet. Exp. Fluids 57 (5), 84.CrossRefGoogle Scholar
Jordan, P. & Colonius, T. 2013 Wave packets and turbulent jet noise. Annu. Rev. Fluid Mech. 45 (1), 173–195.CrossRefGoogle Scholar
Knast, T., Bell, G., Wong, M., Leb, C.M., Soria, J., Honnery, D.R. & Edgington-Mitchell, D. 2018 Coupling modes of an underexpanded twin axisymmetric jet. AIAA J. 56 (9), 3524–3535.CrossRefGoogle Scholar
Lajús, F.C., Sinha, A., Cavalieri, A.V.G., Deschamps, C.J. & Colonius, T. 2019 Spatial stability analysis of subsonic corrugated jets. J. Fluid Mech. 876, 766–791.CrossRefGoogle Scholar
Mancinelli, M., Jaunet, V., Jordan, P. & Towne, A. 2019 Screech-tone prediction using upstream-travelling jet modes. Exp. Fluids 60 (1), 22.CrossRefGoogle Scholar
Marant, M. & Cossu, C. 2018 Influence of optimally amplified streamwise streaks on the Kelvin–Helmholtz instability. J. Fluid Mech. 838, 478–500.CrossRefGoogle Scholar
Merle, M. 1956 Sur la frequence des ondes sonores emises par un jet dair a grande vitesse. C. R. Acad. Sci. 243 (5), 490–493.Google Scholar
Michalke, A. 1965 On spatially growing disturbances in an inviscid shear layer. J. Fluid Mech. 23 (3), 521–544.CrossRefGoogle Scholar
Michalke, A. 1970 A wave model for sound generation in circular jets. Tech. Rep.. Deutsche Luft- und Raumfahrt.Google Scholar
Mollo-Christensen, E. 1967 Jet noise and shear flow instability seen from an experimenter's viewpoint (similarity laws for jet noise and shear flow instability as suggested by experiments). J. Appl. Mech. 34, 1–7.CrossRefGoogle Scholar
Morris, P.J. 1990 Instability waves in twin supersonic jets. J. Fluid Mech. 220, 293–307.CrossRefGoogle Scholar
Nichols, J.W. & Lele, S.K. 2011 Global modes and transient response of a cold supersonic jet. J. Fluid Mech. 669 (1), 225–241.CrossRefGoogle Scholar
Nogueira, P.A.S. & Cavalieri, A.V.G. 2021 Dynamics of shear-layer coherent structures in a forced wall-bounded flow. J. Fluid Mech. 907, A32.CrossRefGoogle Scholar
Norum, T.D. & Shearin, J.G. 1986 Dynamic loads on twin jet exhaust nozzles due to shock noise. J. Aircraft 23 (9), 728–729.CrossRefGoogle Scholar
Oberleithner, K., Sieber, M., Nayeri, C.N., Paschereit, C.O., Petz, C., Hege, H.-C., Noack, B.R. & Wygnanski, I. 2011 Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction. J. Fluid Mech. 679, 383–414.CrossRefGoogle 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.CrossRefGoogle Scholar
Pickering, E., Rigas, G., Schmidt, O.T., Sipp, D. & Colonius, T. 2020 Optimal eddy viscosity for resolvent-based models of coherent structures in turbulent jets. arXiv:2005.10964CrossRefGoogle Scholar
Powell, A. 1953 a The noise of choked jets. J. Acoust. Soc. Am. 25 (3), 385–389.CrossRefGoogle Scholar
Powell, A. 1953 b On the mechanism of choked jet noise. Proc. Phys. Soc. B 66 (12), 1039–1056.CrossRefGoogle Scholar
Raman, G. 1998 Advances in understanding supersonic jet screech: review and perspective. Prog. Aerosp. Sci. 34 (1), 45–106.CrossRefGoogle Scholar
Rodríguez, D., Jotkar, M.R. & Gennaro, E.M. 2018 Wavepacket models for subsonic twin jets using 3d parabolized stability equations. C. R. Mécanique 346 (10), 890–902.CrossRefGoogle Scholar
Sano, A., Abreu, L.I., Cavalieri, A.V.G. & Wolf, W.R. 2019 Trailing-edge noise from the scattering of spanwise-coherent structures. Phys. Rev. Fluids 4, 094602.CrossRefGoogle Scholar
Seiner, J.M., Manning, J.C. & Ponton, M.K. 1988 Dynamic pressure loads associated with twin supersonic plume resonance. AIAA J. 26 (8), 954–960.CrossRefGoogle Scholar
Shen, H. & Tam, C.K.W. 2002 Three-dimensional numerical simulation of the jet screech phenomenon. AIAA J. 40 (1), 33–41.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
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. I. Coherent structures. Q. Appl. Maths 45, 561–571.CrossRefGoogle Scholar
Taira, K., Brunton, S.L., Dawson, S.T.M., Rowley, C.W., Colonius, T., McKeon, B.J., Schmidt, O.T., Gordeyev, S., Theofilis, V. & Ukeiley, L.S. 2017 Modal analysis of fluid flows: an overview. AIAA J. 55 (12), 4013–4041.CrossRefGoogle Scholar
Taira, K., Hemati, M.S., Brunton, S.L., Sun, Y., Duraisamy, K., Bagheri, S., Dawson, S.T.M. & Yeh, C.A. 2020 Modal analysis of fluid flows: applications and outlook. AIAA J. 58 (3), 998–1022.CrossRefGoogle Scholar
Tam, C.K.W. 1995 Supersonic jet noise. Annu. Rev. Fluid Mech. 27 (1), 17–43.CrossRefGoogle 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. & Tanna, H.K. 1982 Shock associated noise of supersonic jets from convergent-divergent nozzles. J. Sound Vib. 81 (3), 337–358.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
Van Oudheusden, B.W., Scarano, F., Roosenboom, E.W.M., Casimiri, E.W.F. & Souverein, L.J. 2007 Evaluation of integral forces and pressure fields from planar velocimetry data for incompressible and compressible flows. Exp. Fluids 43 (2-3), 153–162.CrossRefGoogle Scholar
Weideman, J.A. & Reddy, S.C. 2000 A MATLAB differentiation matrix suite. ACM Trans. Math. Softw. 26 (4), 465–519.CrossRefGoogle Scholar
Weightman, J.L., Amili, O., Honnery, D., Soria, J. & Edgington-Mitchell, D. 2018 Signatures of shear-layer unsteadiness in proper orthogonal decomposition. Exp. Fluids 59 (12), 180.CrossRefGoogle Scholar