Wavepacket models for subsonic twin jets using 3D parabolized stability equations

Daniel Rodríguez; Mamta R. Jotkar; Elmer M. Gennaro

doi:10.1016/j.crme.2018.07.002

Wavepacket models for subsonic twin jets using 3D parabolized stability equations

Daniel Rodríguez ¹ ; Mamta R. Jotkar ²; Elmer M. Gennaro ³

¹ Laboratory of Theoretical and Applied Mechanics (LMTA), Graduate Program in Mechanical Engineering (PGMEC), Department of Mechanical Engineering, Universidade Federal Fluminense, Niterói, RJ 24210-240, Brazil
² Centro Tecnológico, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ 21941-914, Brazil
³ São Paulo State University (UNESP), Campus São João da Boa Vista, SP 13874-149, Brazil

Comptes Rendus. Mécanique, Volume 346 (2018) no. 10, pp. 890-902.

Abstract

An extension of the classical parabolized stability equations to flows strongly dependent on the two cross-stream spatial directions and weakly dependent on the streamwise one is applied to model the large-scale structures present in twin-jet configurations. The existence of these unsteady flow structures, usually referred to as wavepackets, has been demonstrated in the literature for both subsonic and supersonic round jets, along with their relation to the generation of highly directional noise emitted in the aft direction. The present study considers twin-jet configurations with different separations at high Reynolds number and subsonic conditions. The existing instability modes for the twin-jet mean flow, their dependence on the separation of the two jets, and the interaction between the wavepackets originating from the two jets is investigated here. Arising from the axisymmetric mode for single round jets, two dominant modes are found for twin jets: a varicose one, relatively insensitive to jets' proximity, but likely to be efficient in radiating noise; a sinuous one, whose amplification is strongly dependent on the jets' distance, and which can be expected to produce weaker acoustic signatures.

Received: 2017-06-14
Accepted: 2018-01-03
Published online: 2018-07-19

DOI: 10.1016/j.crme.2018.07.002

Keywords: Twin jets, Flow instability, Parabolized Stability Equations, Wavepackets, Turbulence modelling

Author's affiliations:

Daniel Rodríguez ¹; Mamta R. Jotkar ²; Elmer M. Gennaro ³

¹ Laboratory of Theoretical and Applied Mechanics (LMTA), Graduate Program in Mechanical Engineering (PGMEC), Department of Mechanical Engineering, Universidade Federal Fluminense, Niterói, RJ 24210-240, Brazil
² Centro Tecnológico, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ 21941-914, Brazil
³ São Paulo State University (UNESP), Campus São João da Boa Vista, SP 13874-149, Brazil

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     author = {Daniel Rodr{\'\i}guez and Mamta R. Jotkar and Elmer M. Gennaro},
     title = {Wavepacket models for subsonic twin jets using {3D} parabolized stability equations},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {890--902},
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     doi = {10.1016/j.crme.2018.07.002},
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Daniel Rodríguez; Mamta R. Jotkar; Elmer M. Gennaro. Wavepacket models for subsonic twin jets using 3D parabolized stability equations. Comptes Rendus. Mécanique, Volume 346 (2018) no. 10, pp. 890-902. doi : 10.1016/j.crme.2018.07.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.07.002/

References
Cited by

[1] E. Mollo-Christensen Jet noise and shear flow instability seen from an experimenter's viewpoint, J. Appl. Mech., Volume 34 (1967), pp. 1-7

[2] P. Jordan; T. Colonius Wave packets and turbulent jet noise, Annu. Rev. Fluid Mech., Volume 45 (2013) no. 1, pp. 173-195

[3] D.G. Crighton; P. Huerre Shear-layer pressure fluctuations and superdirective acoustic sources, J. Fluid Mech., Volume 220 (1990), pp. 355-368

[4] C.K.W. Tam Supersonic jet noise, Annu. Rev. Fluid Mech., Volume 27 (1995) no. 1, pp. 17-43

[5] A.V.G. Cavalieri; P. Jordan; T. Colonius; Y. Gervais Axisymmetric superdirectivity in subsonic jets, J. Fluid Mech., Volume 704 (2012), pp. 388-420

[6] D. Juvé; M. Sunyach; G. Compte-Bellot Intermittency in the noise emission in subsonic cold jets, J. Sound Vib., Volume 71 (1980), pp. 319-332

[7] J.I. Hileman; B.S. Thurow; E.J. Caraballo; M. Samimy Large-scale structure evolution and sound emission in high-speeds jets: real-time visualization with simultaneous acoustic measurements, J. Fluid Mech., Volume 544 (2005), pp. 277-307

[8] A.V.G. Cavalieri; G. Daviller; P. Comte; P. Jordan; G. Tadmor; Y. Gervais Using large eddy simulation to explore sound-source mechanisms in jets, J. Sound Vib. (2011) no. 330, pp. 4098-4113

[9] S. Crow; F. Champagne Orderly structure in jet turbulence, J. Fluid Mech., Volume 48 (1971) no. 3, pp. 547-591

[10] D.G. Crighton; M. Gaster Stability of slowly diverging jet flow, J. Fluid Mech., Volume 77 (1976) no. 2, pp. 397-413

[11] A. Michalke Survey on jet instability theory, Prog. Aerosp. Sci., Volume 21 (1984), pp. 159-199

[12] T. Suzuki; T. Colonius Instability waves in a subsonic round jet detected using a near-field phased microphone array, J. Fluid Mech., Volume 565 (2006), pp. 197-226

[13] K. Gudmundsson; T. Colonius Instability wave models for the near-field fluctuations of turbulent jets, J. Fluid Mech., Volume 689 (2011), pp. 97-128

[14] A.V.G. Cavalieri; D. Rodríguez; P. Jordan; T. Colonius; Y. Gervais Wavepackets in the velocity field of turbulent jets, J. Fluid Mech., Volume 730 (2013), pp. 559-592

[15] E. Piot; G. Casalis; F. Muller; C. Bailly Investigation of the PSE approach for subsonic and supersonic hot jets. Detailed comparisons with LES and linearized Euler equations results, Int. J. Aeroacoust., Volume 5 (2006), pp. 361-393

[16] P.K. Ray; L.C. Cheung; S.K. Lele On the growth and propagation of linear instability waves in compressible turbulent jets, Phys. Fluids, Volume 21 (2009)

[17] D. Rodríguez; A. Sinha; G. Brès; T. Colonius Inlet conditions for wave packet models in turbulent jets based on eigenmode decomposition of large eddy simulation data, Phys. Fluids, Volume 25 (2013)

[18] A. Sinha; D. Rodríguez; G. Brès; T. Colonius Wavepacket models for supersonic jet noise, J. Fluid Mech., Volume 742 (2014), pp. 71-95

[19] J.W. Nichols; S.K. Lele Global modes and transient response of a cold supersonic jet, J. Fluid Mech., Volume 669 (2011), pp. 225-241

[20] X. Garnaud; L. Lesshafft; P.J. Schmid; P. Huerre Modal and transient dynamics of jet flows, Phys. Fluids, Volume 25 (2013)

[21] X. Garnaud; L. Lesshafft; P.J. Schmid; P. Huerre The preferred mode of incompressible jets: linear frequency response analysis, J. Fluid Mech., Volume 716 (2013), pp. 189-202

[22] A. Towne; T. Colonius One-way spatial integration of hyperbolic equations, J. Comput. Phys., Volume 300 (2015), pp. 844-861

[23] W.V. Bhat Acoustic Characteristics of Two Parallel Flow Jets, 1977 (AIAA Paper 77-1290)

[24] R.A. Kantola Acoustic properties of heated twin jets, J. Sound Vib., Volume 79 (1981) no. 1, pp. 79-106

[25] P.J. Morris Instability waves in twin supersonic jets, J. Fluid Mech., Volume 220 (1990), pp. 293-307

[26] M.R. Green; D.G. Crighton Instability properties of interacting jets, J. Fluid Mech., Volume 350 (1997), pp. 331-349

[27] M. Broadhurst; S. Sherwin The parabolised stability equations for 3D-flows: implementation and numerical stability, Appl. Numer. Math., Volume 58 (2008) no. 7, pp. 1017-1029

[28] D. Rodríguez; A.V.G. Cavalieri; T. Colonius; P. Jordan A study of linear wavepacket models for subsonic turbulent jets using local eigenmode decomposition of PIV data, Eur. J. Mech. B, Fluids, Volume 49 (2015), pp. 308-321

[29] F.P. Bertolotti; Th. Herbert; P.R. Spalart Linear and nonlinear stability of the Blasius boundary layer, J. Fluid Mech., Volume 242 (1992), pp. 441-474

[30] C-L. Chang; M.R. Malik; G. Erlenbacher; M.Y. Hussaini Linear and Nonlinear PSE for Compressible Boundary Layers, 1993 (ICASE Report No. 93-70)

[31] T. Herbert Parabolized stability equations, Annu. Rev. Fluid Mech., Volume 29 (1997), pp. 245-283

[32] L.M. Mack, Boundary layer linear stability theory, AGARD-R-709 Special course on stability and transition of laminar flow, 1984, 3.1–3.81.

[33] P. Balakumar; M.R. Malik Discrete modes and continuous spectra in supersonic boundary layer, J. Fluid Mech., Volume 239 (1992), pp. 631-656

[34] D. Rodríguez; V. Theofilis Massively parallel numerical solution of the biglobal linear instability eigenvalue problem using dense linear algebra, AIAA J., Volume 47 (2009) no. 10, pp. 2449-2459

[35] V. Theofilis Global linear stability, Annu. Rev. Fluid Mech., Volume 43 (2011), pp. 319-352

[36] E.M. Gennaro; D. Rodríguez; M.A.F. Medeiros; V. Theofilis Sparse techniques in global flow instability with application to compressible leading-edge flow, AIAA J., Volume 51 (2013) no. 9, pp. 2295-2303

[37] D. Rodríguez; E.M. Gennaro Three-dimensional flow stability analysis based on the matrix-forming approach made affordable (J.S. Hesthaven, ed.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016, Lect. Notes Comput. Sci. Eng., vol. 199, Springer, 2017

[38] W.E. Arnoldi The principle of minimized iterations in the solution of the matrix eigenvalue problem, Q. Appl. Math., Volume 9 (1951), pp. 17-29

[39] G.H. Golub; C.F. Van Loan Matrix Computations, Johns Hopkins University Press, 1996

[40] P.R. Amestoy; I.S. Duff; J.-Y. L'Excellent; J. Koster A fully asynchronous multifrontal solver using distributed dynamic scheduling, SIAM J. Matrix Anal. Appl., Volume 23 (2001) no. 1, pp. 15-41

[41] F. Li; M.R. Malik Spectral analysis of parabolized stability equations, Comput. Fluids, Volume 26 (1997) no. 3, pp. 279-297

[42] P. Andersson; D.S. Henningson; A. Hanifi On a stabilization procedure for the parabolic stability equations, J. Eng. Math., Volume 33 (1998), pp. 311-332

[43] T.R. Troutt; D.K. McLaughlin Experiments on the flow and acoustic properties of a moderate Reynolds number supersonic jet, J. Fluid Mech., Volume 116 (1982), pp. 123-156

[44] C.K.W. Tam; D.E. Burton Sound generated by instability waves of supersonic flows. Part 2. Axisymmetric jets, J. Fluid Mech., Volume 138 (1984), pp. 273-295

[45] T. Okamoto; M. Yagita; A. Watanabe; K. Kawamura Interaction of twin turbulent circular jets, Bull. JSME, Volume 28 (1985) no. 238, pp. 617-622

[46] A.E. Gill Instabilities of Top-Hat jets and wakes in compressible fluids, Phys. Fluids, Volume 8 (1965), pp. 1428-1430

[47] A. Towne; T. Colonius; P. Jordan; A.V.G. Cavalieri; G. Brès Stochastic and nonlinear forcing of wavepackets in a Mach 0.9 jet, 21st AIAA/CEAS Aeroacoustics Conference, AIAA, Dallas, TX, 2015

[48] O. Semeraro; V. Jaunet; P. Jordan; A.V.G. Cavalieri; L. Lesshafft Stochastic and harmonic optimal forcing in subsonic jets, 22nd AIAA/CEAS Aeroacoustics Conference, AIAA, Lyon, France, 2016

[49] D.E.S. Breakey; P. Jordan; A.V.G. Cavalieri; P.A. Nogueira; O. Léon; T. Colonius; D. Rodríguez Experimental study of turbulent-jet wave packets and their acoustic efficiency, Phys. Rev. Fluids, Volume 2 (2017)

[50] S. Beneddine; D. Sipp; A. Arnault; J. Dandois; L. Lesshafft Conditions for validity of mean flow stability analysis, J. Fluid Mech., Volume 798 (2016), pp. 485-504

[51] W.R. Wolf; J.L.F. Azevedo; S.K. Lele Convective effects and the role of quadrupole sources for aerofoil aeroacoustics, J. Fluid Mech., Volume 708 (2012), pp. 502-538

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