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.

Accepted:

Published online:

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

@article{CRMECA_2018__346_10_890_0, 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}, publisher = {Elsevier}, volume = {346}, number = {10}, year = {2018}, doi = {10.1016/j.crme.2018.07.002}, language = {en}, }

TY - JOUR AU - Daniel Rodríguez AU - Mamta R. Jotkar AU - Elmer M. Gennaro TI - Wavepacket models for subsonic twin jets using 3D parabolized stability equations JO - Comptes Rendus. Mécanique PY - 2018 SP - 890 EP - 902 VL - 346 IS - 10 PB - Elsevier DO - 10.1016/j.crme.2018.07.002 LA - en ID - CRMECA_2018__346_10_890_0 ER -

%0 Journal Article %A Daniel Rodríguez %A Mamta R. Jotkar %A Elmer M. Gennaro %T Wavepacket models for subsonic twin jets using 3D parabolized stability equations %J Comptes Rendus. Mécanique %D 2018 %P 890-902 %V 346 %N 10 %I Elsevier %R 10.1016/j.crme.2018.07.002 %G en %F CRMECA_2018__346_10_890_0

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/

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

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

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

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

[5] Axisymmetric superdirectivity in subsonic jets, J. Fluid Mech., Volume 704 (2012), pp. 388-420

[6] Intermittency in the noise emission in subsonic cold jets, J. Sound Vib., Volume 71 (1980), pp. 319-332

[7] 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] Using large eddy simulation to explore sound-source mechanisms in jets, J. Sound Vib. (2011) no. 330, pp. 4098-4113

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

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

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

[12] 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] Instability wave models for the near-field fluctuations of turbulent jets, J. Fluid Mech., Volume 689 (2011), pp. 97-128

[14] Wavepackets in the velocity field of turbulent jets, J. Fluid Mech., Volume 730 (2013), pp. 559-592

[15] 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] On the growth and propagation of linear instability waves in compressible turbulent jets, Phys. Fluids, Volume 21 (2009)

[17] Inlet conditions for wave packet models in turbulent jets based on eigenmode decomposition of large eddy simulation data, Phys. Fluids, Volume 25 (2013)

[18] Wavepacket models for supersonic jet noise, J. Fluid Mech., Volume 742 (2014), pp. 71-95

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

[20] Modal and transient dynamics of jet flows, Phys. Fluids, Volume 25 (2013)

[21] The preferred mode of incompressible jets: linear frequency response analysis, J. Fluid Mech., Volume 716 (2013), pp. 189-202

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

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

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

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

[26] Instability properties of interacting jets, J. Fluid Mech., Volume 350 (1997), pp. 331-349

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

[28] 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] Linear and nonlinear stability of the Blasius boundary layer, J. Fluid Mech., Volume 242 (1992), pp. 441-474

[30] Linear and Nonlinear PSE for Compressible Boundary Layers, 1993 (ICASE Report No. 93-70)

[31] 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] Discrete modes and continuous spectra in supersonic boundary layer, J. Fluid Mech., Volume 239 (1992), pp. 631-656

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

[36] Sparse techniques in global flow instability with application to compressible leading-edge flow, AIAA J., Volume 51 (2013) no. 9, pp. 2295-2303

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

[39] Matrix Computations, Johns Hopkins University Press, 1996

[40] A fully asynchronous multifrontal solver using distributed dynamic scheduling, SIAM J. Matrix Anal. Appl., Volume 23 (2001) no. 1, pp. 15-41

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

[42] On a stabilization procedure for the parabolic stability equations, J. Eng. Math., Volume 33 (1998), pp. 311-332

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

[44] Sound generated by instability waves of supersonic flows. Part 2. Axisymmetric jets, J. Fluid Mech., Volume 138 (1984), pp. 273-295

[45] Interaction of twin turbulent circular jets, Bull. JSME, Volume 28 (1985) no. 238, pp. 617-622

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

[47] Stochastic and nonlinear forcing of wavepackets in a Mach 0.9 jet, 21st AIAA/CEAS Aeroacoustics Conference, AIAA, Dallas, TX, 2015

[48] Stochastic and harmonic optimal forcing in subsonic jets, 22nd AIAA/CEAS Aeroacoustics Conference, AIAA, Lyon, France, 2016

[49] Experimental study of turbulent-jet wave packets and their acoustic efficiency, Phys. Rev. Fluids, Volume 2 (2017)

[50] Conditions for validity of mean flow stability analysis, J. Fluid Mech., Volume 798 (2016), pp. 485-504

[51] Convective effects and the role of quadrupole sources for aerofoil aeroacoustics, J. Fluid Mech., Volume 708 (2012), pp. 502-538

*Cited by Sources: *

Comments - Policy