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A study of linear wavepacket models for subsonic turbulent jets using local eigenmode decomposition of PIV data. (English) Zbl 1408.76227
Summary: Locally-parallel linear stability theory (LST) of jet velocity profiles is revisited to study the evolution of the wavepackets and the manner in which the parabolized stability equations (PSE) approach models them. An adjoint-based eigenmode decomposition technique is used to project cross-sectional velocity profiles measured using time-resolved particle image velocimetry (PIV) on the different families of eigenmodes present in the LST eigenspectrum. Attention is focused on the evolution of the Kelvin-Helmholtz (K-H) eigenmode and the projection of experimental fluctuations on it, since in subsonic jets the inflectional K-H instability is the only possible mechanism for linear amplification of the large-scale fluctuations, and governs the wavepacket evolution. Comparisons of the fluctuations extracted by projection onto K-H eigenmode with PSE solutions and PIV measurements are made. We show that the jet can be divided into three main regions, classified with respect to the LST eigenspectrum. Near the jet exit, there is significant amplification of the K-H mode; the PSE solution is shown to comprise almost exclusively the K-H mode, and the agreement with experiments shows that the evolution of this mode dominates the near-nozzle fluctuations. For downstream positions, the Kelvin-Helmholtz mode becomes stable and eventually merges with other branches of the eigenspectrum. The comparison between PSE, experiment and the projection onto the K-H mode for downstream positions suggests that the mechanism of saturation and decay of wavepackets is related to a combination of several marginally stable modes, which is reasonably well modeled by linear PSE, but cannot be obtained in the usual application of locally-parallel stability dealing exclusively with the K-H mode. In addition, the projection of empirical data on the K-H eigenmode at a near-nozzle cross-section is shown to be a well-founded method for the determination of the amplitudes of the linear wavepacket models.

MSC:
76D25 Wakes and jets
76Q05 Hydro- and aero-acoustics
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[1] Lighthill, M. J., On sound generated aerodynamically. I. general theory, Proc. R. Soc. Lond. A., 222, 1148, 1-32, (1954) · Zbl 0055.19109
[2] Jordan, P.; Colonius, T., Wave packets and turbulent jet noise, Annu. Rev. Fluid Mech., 45, 1, 173-195, (2013) · Zbl 1359.76257
[3] Mollo-Christensen, E., Jet noise and shear flow instability seen from an experimenter’s viewpoint, J. Appl. Mech., 34, 1-7, (1967)
[4] Crow, S. C.; Champagne, F. H., Orderly structure in jet turbulence, J. Fluid Mech., 3, 547-591, (1971)
[5] Michalke, A., Instabilititat eines kompressiblen runden freistrahls unter berucksichtigung des einflusses der strahlgrenzschichtdicke, Z. Flugwissenschaften, 19, 319-328, (1971) · Zbl 0224.76050
[6] Crighton, D. G.; Gaster, M., Stability of slowly diverging jet flow, J. Fluid Mech., 77, 2, 397-413, (1976) · Zbl 0338.76021
[7] Plaschko, P., Helical instabilities of slowly diverging flows. part 2, J. Fluid Mech., 92, 209-215, (1979) · Zbl 0398.76040
[8] Tam, C. K.W.; Burton, D. E., Sound generated by instability waves of supersonic flows. part 2. axisymmetric jets, J. Fluid Mech., 138, 273-295, (1984) · Zbl 0543.76109
[9] P. Balakumar, Prediction of supersonic jet noise, AIAA Paper 1998-1057.
[10] Malik, M. R.; Chang, C. L., Nonparallel and nonlinear stability of supersonic jet flow, Comput. & Fluids, 29, 327-365, (2000) · Zbl 0978.76030
[11] Piot, E.; Casalis, G.; Muller, F.; Bailly, C., Investigation of the PSE approach for subsonic and supersonic hot jets. detailed comparisons with LES and linearized Euler equations results, Int. J. Aeroacoustics, 5, 361-393, (2006)
[12] Gudmundsson, K.; Colonius, T., Instability wave models for the near-field fluctuations of turbulent jets, J. Fluid Mech., 689, 97-128, (2011) · Zbl 1241.76203
[13] Cavalieri, A. V.G.; Rodríguez, D.; Jordan, P.; Colonius, T.; Gervais, Y., Wavepackets in the velocity field of turbulent jets, J. Fluid Mech., 730, 559-592, (2013) · Zbl 1291.76280
[14] Nichols, J. W.; Lele, S. K., Global modes and transient response of a cold supersonic jet, J. Fluid Mech., 669, 225-241, (2011) · Zbl 1225.76116
[15] Liu, J. T.C., Developing large-scale wavelike eddies and the near jet noise field, J. Fluid Mech., 62, 437-464, (1974) · Zbl 0276.76026
[16] Mankbadi, R.; Liu, J. T.C., A study of the interactions between large-scale coherent structures and fine-grained turbulence in a round jet, Proc. Roy. Soc. London, 1443, 541-602, (1981) · Zbl 0464.76045
[17] Morris, P. J.; Giridharan, M. G.; Lilley, G. M., On the turbulent mixing of compressible free shear layers, Proc. R. Soc. Lond. A., 431, 219-243, (1990) · Zbl 0711.76043
[18] Suzuki, T.; Colonius, T., Instability waves in a subsonic round jet detected using a near-field phased microphone array, J. Fluid Mech., 565, 197-226, (2006) · Zbl 1104.76023
[19] J. Bridges, M. Wernet, Measurements of the aeroacoustic sound source in hot jets, AIAA Paper 2003-3130.
[20] Tinney, C. E.; Jordan, P., The near pressure field of co-axial subsonic jets, J. Fluid Mech., 611, 175-204, (2008) · Zbl 1151.76356
[21] D.E.S. Breakey, P. Jordan, A.V.G. Cavalieri, O. Léon, M. Zhang, G. Lehnasch, T. Colonius, D. Rodríguez, Near-field wavepackets and the far-field sound of a subsonic jet, AIAA Paper 2013-2083.
[22] Michalke, A.; Fuchs, H. V., On turbulence and noise of an axisymmetric shear flow, J. Fluid Mech., 70, 179-205, (1975) · Zbl 0312.76051
[23] Laufer, J.; Yen, T. C., Noise generation by a low-Mach-number jet, J. Fluid Mech., 134, 1-31, (1983)
[24] Kerhervé, F.; Jordan, P.; Cavalieri, A. V.G.; Delville, J.; Bogey, C.; Juvé, D., Educing the source mechanism associated with the downstream radiation in subsonic jets, J. Fluid Mech., 710, 606-640, (2012) · Zbl 1275.76185
[25] Tumin, A.; Amitay, M.; Cohen, J.; Zhou, M. D., A normal multimode decomposition method for stability experiments, Phys. Fluids, 8, 10, 2777-2779, (1996)
[26] Tumin, A.; Wang, X.; Zhong, X., Direct numerical simulation and the theory of receptivity in a hypersonic boundary layer, Phys. Fluids, 19, 11, 014101, (2007) · Zbl 1146.76556
[27] Rodríguez, D.; Sinha, A.; Brès, G. A.; Colonius, T., Inlet conditions for wave packet models in turbulent jets based on eigenmode decomposition of LES data, Phys. Fluids, 25, 105107, (2013)
[28] Cavalieri, A. V.G.; Jordan, P.; Colonius, T.; Gervais, Y., Axisymmetric superdirectivity in subsonic jets, J. Fluid Mech., 704, 388-420, (2012) · Zbl 1246.76005
[29] Morris, P. J., The spatial viscous instability of axisymmetric jets, J. Fluid Mech., 77, part 3, 511-529, (1976) · Zbl 0358.76036
[30] Schlichting, H., Boundary layer theory, (1979), McGraw-Hill
[31] Sinha, A.; Rodríguez, D.; Brès, G. A.; Colonius, T., Wavepacket models for supersonic jet noise, J. Fluid Mech., 742, 71-95, (2014)
[32] Herbert, T., Parabolized stability equations, Annu. Rev. Fluid Mech., 29, 245-283, (1997)
[33] K. Gudmundsson, Instability wave models of turbulent jets from round and serrated nozzles, Ph.D. Thesis, California Institute of Technology, 2010.
[34] Thompson, K. W., Time dependent boundary conditions for hyperbolic systems, J. Comput. Phys., 68, 1-24, (1987) · Zbl 0619.76089
[35] Mohseni, K.; Colonius, T., Numerical treatment of polar coordinate singularities, J. Comput. Phys., 157, 787-795, (2000) · Zbl 0981.76075
[36] Li, F.; Malik, M. R., Spectral analysis of parabolized stability equations, Comp. Fluids, 26, 3, 279-297, (1997) · Zbl 0886.76029
[37] Salwen, H.; Grosch, C. E., The continuous spectrum of the Orr-Sommerfeld equation. part II. eigenfunction expansions, J. Fluid Mech., 104, 445-465, (1981) · Zbl 0467.76051
[38] Tumin, A. M.; Fedorov, A. V., Spatial growth of disturbances in a compressible boundary layer, J. Appl. Mech. Tech. Phys., 24, 548-554, (1983)
[39] Chomaz, J., Global instabilities in spatially developing flows: non-normality and nonlinearity, Ann. Rev. Fluid Mech., 37, 357-392, (2005) · Zbl 1117.76027
[40] Schmid, P., Nonmodal stability thoeory, Ann. Rev. Fluid Mech., 39, 129-162, (2007) · Zbl 1296.76055
[41] Hill, D. C., Adjoint systems and their role in the receptivity problem for boundary layers, J. Fluid Mech., 292, 183-204, (1995) · Zbl 0866.76029
[42] Tumin, A., Three-dimensional spatial normal modes in compressible boundary layers, J. Fluid Mech., 586, 295-322, (2007) · Zbl 1119.76051
[43] D. Rodríguez, A. Sinha, G.A. Brès, T. Colonius, Acoustic field associated with parabolized stability equations models in turbulent jets, AIAA Paper 2013-2279.
[44] Gill, A. E., Instabilities of top-hat jets and wakes in compressible fluids, Phys. Fluids, 8, 1428-1430, (1965)
[45] Tam, C. K.W.; Hu, F. Q., On the three families of instability waves of high-speed jets, J. Fluid Mech., 201, 447-483, (1989) · Zbl 0672.76054
[46] F.P. Bertolotti, T. Colonius, On the noise generated by convected structures in a Mach 0.9 hot, turbulent jet, AIAA Paper 2003-1062.
[47] Michalke, A., Survey on jet instability theory, Prog. Aerospace Sci., 21, 159-199, (1984)
[48] Lumley, J. L., The structure of inhomogeneous turbulent flows, (Atmospheric Turbulence and Radio Wave Propagation, (1967), Nauka), 116-178
[49] Arndt, R. E.A.; Long, D.; Glauser, M., The proper orthogonal decomposition of pressure fluctuations surrounding a turbulent jet, J. Fluid Mech., 340, 1-33, (1997)
[50] Strange, P. J.R.; Crighton, D. G., Spinning modes on axisymmetric jets. part 1, J. Fluid Mech., 134, 231-245, (1983)
[51] Suponitsky, V.; Sandham, N. D.; Morfey, C. L., Linear and nonlinear mechanisms of sound radiation by instability waves in subsonic jets, J. Fluid Mech., 658, 509-538, (2010) · Zbl 1205.76242
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