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Effects of nozzle-exit boundary-layer profile on the initial shear-layer instability, flow field and noise of subsonic jets

  • Christophe Bogey (a1) and Roberto Sabatini (a2)


The influence of the nozzle-exit boundary-layer profile on high-subsonic jets is investigated by performing compressible large-eddy simulations (LES) for three isothermal jets at a Mach number of 0.9 and a diameter-based Reynolds number of $5\times 10^{4}$ , and by conducting linear stability analyses from the mean-flow fields. At the exit section of a pipe nozzle, the jets exhibit boundary layers of momentum thickness of approximately 2.8 % of the nozzle radius and a peak value of turbulence intensity of 6 %. The boundary-layer shape factors, however, vary and are equal to 2.29, 1.96 and 1.71. The LES flow and sound fields differ significantly between the first jet with a laminar mean exit velocity profile and the two others with transitional profiles. They are close to each other in these two cases, suggesting that similar results would also be obtained for a jet with a turbulent profile. For the two jets with non-laminar profiles, the instability waves in the near-nozzle region emerge at higher frequencies, the mixing layers spread more slowly and contain weaker low-frequency velocity fluctuations and the noise levels in the acoustic field are lower by 2–3 dB compared to the laminar case. These trends can be explained by the linear stability analyses. For the laminar boundary-layer profile, the initial shear-layer instability waves are most strongly amplified at a momentum-thickness-based Strouhal number $St_{\unicode[STIX]{x1D703}}=0.018$ , which is very similar to the value obtained downstream in the mixing-layer velocity profiles. For the transitional profiles, on the contrary, they predominantly grow at higher Strouhal numbers, around $St_{\unicode[STIX]{x1D703}}=0.026$ and 0.032, respectively. As a consequence, the instability waves rapidly vanish during the boundary-layer/shear-layer transition in the latter cases, but continue to grow over a large distance from the nozzle in the former case, leading to persistent large-scale coherent structures in the mixing layers for the jet with a laminar exit velocity profile.

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Ahuja, K. K., Tester, B. J. & Tanna, H. K. 1987 Calculation of far field jet noise spectra from near field measurements with true source location. J. Sound Vib. 116 (3), 415426.
Arndt, R. E. A., Long, D. F. & Glauser, M. N. 1997 The proper orthogonal decomposition of pressure fluctuations surrounding a turbulent jet. J. Fluid Mech. 340, 133.
Berland, J., Bogey, C., Marsden, O. & Bailly, C. 2007 High-order, low dispersive and low dissipative explicit schemes for multi-scale and boundary problems. J. Comput. Phys. 224 (2), 637662.
Bogey, C. 2018 Grid sensitivity of flow field and noise of high-Reynolds-number jets computed by large-eddy simulation. Intl J. Aeroacoust. 17 (4-5), 399424.
Bogey, C. 2019 On noise generation in low Reynolds number temporal round jets at a Mach number of 0.9. J. Fluid Mech. 859, 10221056.
Bogey, C. & Bailly, C. 2002 Three-dimensional non-reflective boundary conditions for acoustic simulations: far-field formulation and validation test cases. Acta Acust. United Acust. 88 (4), 463471.
Bogey, C. & Bailly, C. 2004 A family of low dispersive and low dissipative explicit schemes for flow and noise computations. J. Comput. Phys. 194 (1), 194214.
Bogey, C. & Bailly, C. 2006 Large eddy simulations of transitional round jets: influence of the Reynolds number on flow development and energy dissipation. Phys. Fluids 18 (6), 065101.
Bogey, C. & Bailly, C. 2007 An analysis of the correlations between the turbulent flow and the sound pressure field of subsonic jets. J. Fluid Mech. 583, 7197.
Bogey, C. & Bailly, C. 2009 Turbulence and energy budget in a self-preserving round jet: direct evaluation using large-eddy simulation. J. Fluid Mech. 627, 129160.
Bogey, C. & Bailly, C. 2010 Influence of nozzle-exit boundary-layer conditions on the flow and acoustic fields of initially laminar jets. J. Fluid Mech. 663, 507539.
Bogey, C., Barré, S. & Bailly, C. 2008 Direct computation of the noise generated by subsonic jets originating from a straight pipe nozzle. Intl J. Aeroacoust. 7 (1), 122.
Bogey, C., Barré, S., Fleury, V., Bailly, C. & Juvé, D. 2007 Experimental study of the spectral properties of near-field and far-field jet noise. Intl J. Aeroacoust. 6 (2), 7392.
Bogey, C., Barré, S., Juvé, D. & Bailly, C. 2009a Simulation of a hot coaxial jet: direct noise prediction and flow-acoustics correlations. Phys. Fluids 21 (3), 035105.
Bogey, C., de Cacqueray, N. & Bailly, C. 2009b A shock-capturing methodology based on adaptative spatial filtering for high-order non-linear computations. J. Comput. Phys. 228 (5), 14471465.
Bogey, C., de Cacqueray, N. & Bailly, C. 2011a Finite differences for coarse azimuthal discretization and for reduction of effective resolution near origin of cylindrical flow equations. J. Comput. Phys. 230 (4), 11341146.
Bogey, C. & Marsden, O. 2013 Identification of the effects of the nozzle-exit boundary-layer thickness and its corresponding Reynolds number in initially highly disturbed subsonic jets. Phys. Fluids 25 (5), 055106.
Bogey, C. & Marsden, O. 2016 Simulations of initially highly disturbed jets with experiment-like exit boundary layers. AIAA J. 54 (4), 12991312.
Bogey, C., Marsden, O. & Bailly, C. 2011b Large-eddy simulation of the flow and acoustic fields of a Reynolds number 105 subsonic jet with tripped exit boundary layers. Phys. Fluids 23 (3), 035104.
Bogey, C., Marsden, O. & Bailly, C. 2011c On the spectra of nozzle-exit velocity disturbances in initially nominally turbulent jets. Phys. Fluids 23 (9), 091702.
Bogey, C., Marsden, O. & Bailly, C. 2012a Effects of moderate Reynolds numbers on subsonic round jets with highly disturbed nozzle-exit boundary layers. Phys. Fluids 24 (10), 105107.
Bogey, C., Marsden, O. & Bailly, C. 2012b Influence of initial turbulence level on the flow and sound fields of a subsonic jet at a diameter-based Reynolds number of 105 . J. Fluid Mech. 701, 352385.
Bradshaw, P. 1966 The effect of initial conditions on the development of a free shear layer. J. Fluid Mech. 26 (2), 225236.
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, 83124.
Bridges, J. & Brown, C. A.2005 Validation of the small hot jet acoustic rig for aeroacoustics. AIAA Paper 2005-2846.
Bridges, J. E. & Hussain, A. K. M. F. 1987 Roles of initial conditions and vortex pairing in jet noise. J. Sound Vib. 117 (2), 289311.
Browand, F. K. & Latigo, B. O. 1979 Growth of the two-dimensional mixing layer from a turbulent and nonturbulent boundary layer. Phys. Fluids 22 (6), 10111019.
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64 (4), 775816.
Bühler, S., Kleiser, L. & Bogey, C. 2014 Simulation of subsonic turbulent nozzle-jet flow and its near-field sound. AIAA J. 52 (8), 16531669.
Castelain, T.2006 Contrôle de jet par microjets impactants. Mesure de bruit rayonné et analyse aérodynamique. PhD thesis, Ecole Centrale de Lyon, no. 2006-33.
Castillo, L. & Johansson, T. G. 2012 The effects of the upstream conditions on a low Reynolds number turbulent boundary layer with zero pressure gradient. J. Turbul. 3, N31.
Cavalieri, A. V. G., Jordan, P., Colonius, T. & Gervais, Y. 2012 Axisymmetric superdirectivity in subsonic jets. J. Fluid Mech. 704, 388420.
Chandrsuda, C., Mehta, R. D., Weir, A. D. & Bradshaw, P. 1978 Effect of free-stream turbulence on large structure in turbulent mixing layers. J. Fluid Mech. 85 (4), 693704.
Chu, W. T. & Kaplan, R. E. 1976 Use of a spherical concave reflector for jet-noise-source distribution diagnosis. J. Acoust. Soc. Am. 59 (6), 12681277.
Coles, D. E.1962 The turbulent boundary layer in a compressible fluid. Tech. Rep. R-403-PR. Rand Corp.
Crighton, D. G. 1981 Acoustics as a branch of fluid mechanics. J. Fluid Mech. 106, 261298.
Crow, S. C. & Champagne, F. H. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48, 547591.
De Chant, L. J. 2005 The venerable 1/7th power law turbulent velocity profile: a classical nonlinear boundary value problem solution and its relationship to stochastic processes. Appl. Maths Comput. 161 (2), 463474.
Drubka, R. E. & Nagib, H. M.1981 Instabilities in near field of turbulent jets and their dependence on initial conditions and reynolds number. Tech. Rep. R-81-2. IIT Fluids & Heat Transfer Report.
Erm, P. L. & Joubert, P. N. 1991 Low-Reynolds-number turbulent boundary layers. J. Fluid Mech. 230, 144.
Fauconnier, D., Bogey, C. & Dick, E. 2013 On the performance of relaxation filtering for large-eddy simulation. J. Turbul. 14 (1), 2249.
Fernholz, H. H. & Finley, P. J. 1996 The incompressible zero-pressure-gradient turbulent boundary layer: an assessment of the data. Prog. Aerosp. Sci. 32 (4), 245311.
Fieldler, H. E. 1988 Coherent structures in turbulent flows. Prog. Aerosp. Sci. 25, 231269.
Fisher, M. J., Harper-Bourne, M. & Glegg, S. A. L. 1977 Jet engine noise source location: the polar correlation technique. J. Sound Vib. 51 (1), 2354.
Fleury, V.2006 Superdirectivité, bruit d’appariement et autres contributions au bruit de jet subsonique. PhD thesis, Ecole Centrale de Lyon, no. 2006-18.
Fleury, V., Bailly, C., Jondeau, E., Michard, M. & Juvé, D. 2008 Space–time correlations in two subsonic jets using dual particle image velocimetry measurements. AIAA J. 46 (10), 24982509.
Fontaine, R. A., Elliott, G. S., Austin, J. M. & Freund, J. B. 2015 Very near-nozzle shear-layer turbulence and jet noise. J. Fluid Mech. 770, 2751.
Gloerfelt, X. & Berland, J. 2012 Turbulent boundary layer noise: direct radiation at Mach number 0.5. J. Fluid Mech. 723, 318351.
Gutmark, E. & Ho, C.-M. 1983 Preferred modes and the spreading rates of jets. Phys. Fluids 26 (10), 29322938.
Harper-Bourne, M. 2010 Jet noise measurements: past and present. Intl J. Aeroacoust. 9 (4–5), 559588.
Hill, W. G., Jenkins, R. C. & Gilbert, B. L. 1976 Effects of the initial boundary-layer state on turbulent jet mixing. AIAA J. 14 (11), 15131514.
Ho, C. & Huerre, P. 1984 Perturbed free shear layers. Annu. Rev. Fluid Mech. 16, 365422.
Husain, Z. D. & Hussain, A. K. M. F. 1979 Axisymmetric mixing layer: influence of the initial and boundary conditions. AIAA J. 17 (1), 4855.
Hussain, A. K. M. F. 1986 Coherent structures and turbulence. J. Fluid Mech. 173, 303356.
Hussain, A. K. M. F. & Zaman, K. B. M. Q. 1985 An experimental study of organized motions in the turbulent plane mixing layer. J. Fluid Mech. 159, 85104.
Hussain, A. K. M. F. & Zedan, M. F. 1978a Effects of the initial condition on the axisymmetric free shear layer: effects of the initial fluctuation level. Phys. Fluids 21 (9), 14751481.
Hussain, A. K. M. F. & Zedan, M. F. 1978b Effects of the initial condition on the axisymmetric free shear layer: Effects of the initial momentum thickness. Phys. Fluids 21 (7), 11001112.
Hutchings, N. 2012 Caution: tripping hazards. J. Fluid Mech. 710, 14.
Karon, A. Z. & Ahuja, K. K.2013. Effect of nozzle-exit boundary layer on jet noise. AIAA Paper 2013-0615.
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.
Klebanoff, P. S. & Diehl, Z. W.1952. Some features of artificially thickened fully developed turbulent boundary layers with zero pressure gradient. NACA Tech. Rep. 1110.
Kremer, F. & Bogey, C. 2015 Large-eddy simulation of turbulent channel flow using relaxation filtering: resolution requirement and Reynolds number effects. Comput. Fluids 116, 1728.
Lau, J. C., Morris, P. J. & Fisher, M. J. 1979 Measurements in subsonic and supersonic free jets using a laser velocimeter. J. Fluid Mech. 93 (1), 127.
Lee, S. S. & Bridges, J.2005. Phased-array measurements of single flow hot jets. NACA Tech. Rep. 2005-213826.
Lilley, G. M. 1994 Jet noise classical theory and experiments. In Aeroacoustics of Flight Vehicles (ed. Hubbard, H. H.), vol. 1, pp. 211289. Acoustical Society of America.
Lorteau, M., Cléro, F. & Vuillot, F. 2015 Analysis of noise radiation mechanisms in hot subsonic jet from a validated large eddy simulation solution. Phys. Fluids 27 (7), 075108.
Maestrello, L. & McDaid, E. 1971 Acoustic characteristics of a high-subsonic jet. AIAA J. 9 (6), 10581066.
Michalke, A. 1984 Survey on jet instability theory. Prog. Aerosp. Sci. 21, 159199.
Mohseni, K. & Colonius, T. 2000 Numerical treatment of polar coordinate singularities. J. Comput. Phys. 157 (2), 787795.
Mollo-Christensen, E., Kolpin, M. A. & Martucelli, J. R. 1964 Experiments on jet flows and jet noise far-field spectra and directivity patterns. J. Fluid Mech. 18 (2), 285301.
Monty, J. P., Hutchins, N., Ng, H. C. H., Marusic, I. & Chong, M. S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431442.
Morris, P. J. 1976 The spatial viscous instability of axisymmetric jets. J. Fluid Mech. 77 (3), 511529.
Morris, P. J. 2010 The instability of high speed jets. Intl J. Aeroacoust. 9 (1–2), 150.
Morris, P. J. & Zaman, K. B. M. Q. 2009 Velocity measurements in jets with application to noise source modelling. J. Sound Vib. 329 (4), 394414.
Morris, S. C. & Foss, J. F. 2003 Turbulent boundary layer to single-stream shear layer: the transition region. J. Fluid Mech. 494, 187221.
Narayanan, S., Barber, T. J. & Polak, D. R. 2002 High subsonic jet experiments: Turbulence and noise generation studies. AIAA J. 40 (3), 430437.
Panda, J., Seasholtz, R. G. & Elam, K. A. 2005 Investigation of noise sources in high-speed jets via correlation measurements. J. Fluid Mech. 537, 349385.
Raman, G., Rice, E. J. & Reshotko, E. 1994 Mode spectra of natural disturbances in a circular jet and the effect of acoustic forcing. Exp. Fluids 17, 415426.
Raman, G., Zaman, K. B. M. Q. & Rice, E. J. 1989 Initial turbulence effect on jet evolution with and without tonal excitation. Phys. Fluids A 1 (7), 12401248.
Russ, S. & Strykowski, P. J. 1993 Turbulent structure and entrainment in heated jets: the effect of initial conditions. Phys. Fluids A 5 (12), 32163225.
Sabatini, R. & Bailly, C. 2015 Numerical algorithm for computing acoustic and vortical spatial instability waves. AIAA J. 53 (3), 692702.
Sandberg, R. D., Sandham, N. D. & Suponitsky, V. 2012 DNS of compressible pipe flow exiting into a coflow. Intl J. Heat Fluid Flow 35, 3344.
Sato, H. 1971 Experimental investigation on the transition of laminar separated layer. J. Phys. Soc. Japan 48, 702709.
Schlatter, P. & Örlü, R. 2012 Turbulent boundary layers at moderate Reynolds numbers: inflow length and tripping effects. J. Fluid Mech. 710, 534.
Schubauer, G. B. & Klebanoff, P. S.1955. Contributions on the mechanics of boundary-layer transition. NACA Tech. Rep. 3498.
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to r 𝜃 = 1410. J. Fluid Mech. 187, 6198.
Tam, C. K. W. 1998 Jet noise: since 1952. Theor. Comput. Fluid Dyn. 10 (1-4), 393405.
Tam, C. K. W. & Dong, Z. 1996 Radiation and outflow boundary conditions for direct computation of acoustic and flow disturbances in a nonuniform mean flow. J. Comput. Acoust. 4 (2), 175201.
Tam, C. K. W., Viswanathan, K., Ahuja, K. K. & Panda, J. 2008 The sources of jet noise: experimental evidence. J. Fluid Mech. 615, 253292.
Tanna, H. K. 1977 An experimental study of jet noise. Part I: Turbulent mixing noise. J. Sound Vib. 50 (3), 405428.
Tomkins, C. D. & Adrian, R. J. 2005 Energetic spanwise modes in the logarithmic layer of a turbulent boundary layer. J. Fluid Mech. 545, 141162.
Uzun, A. & Hussaini, M. 2007 Investigation of high frequency noise generation in the near-nozzle region of a jet using large eddy simulation. Theor. Comput. Fluid Dyn. 21 (4), 291321.
Viswanathan, K. 2004 Aeroacoustics of hot jets. J. Fluid Mech. 516, 3982.
Viswanathan, K. 2006 Distributions of noise sources in heated and cold jets: are they different? Intl J. Aeroacoust. 9 (4–5), 589625.
Viswanathan, K. & Clark, L. T. 2004 Effect of nozzle internal contour on jet aeroacoustics. Intl J. Aeroacoust. 3 (2), 103135.
Wygnanski, I., Oster, D., Fiedler, H. & Dziomba, B. 1979 On the perseverance of a quasi-two-dimensional eddy-structure in a turbulent mixing layer. J. Fluid Mech. 93 (2), 325335.
Xu, G. & Antonia, R. A. 2002 Effects of different initial conditions on a turbulent free jet. Exp. Fluids 33, 677683.
Yule, A. J. 1978 Large-scale structure in the mixing layer of a round jet. J. Fluid Mech. 89 (3), 413432.
Zaman, K. B. M. Q. 1985a Effect of initial condition on subsonic jet noise. AIAA J. 23 (9), 13701373.
Zaman, K. B. M. Q. 1985b Far-field noise of a subsonic jet under controlled excitation. J. Fluid Mech. 152, 83111.
Zaman, K. B. M. Q. 1986 Flow field and near and far sound field of a subsonic jet. J. Sound Vib. 106 (1), 116.
Zaman, K. B. M. Q. 2012 Effect of initial boundary-layer state on subsonic jet noise. AIAA J. 50 (8), 17841795.
Zaman, K. B. M. Q.2017. Increased jet noise due to a ‘nominally laminar’ state of nozzle exit boundary layer. NASA Tech. Rep. 2017-219440.
Zaman, K. B. M. Q. & Hussain, A. K. M. F. 1981 Turbulence suppression in free shear flows by controlled excitation. J. Fluid Mech. 103, 133159.
Zhu, M., Pérez Arroyo, C., Fosso Pouangué, A., Sanjosé, M. & Moreau, S. 2018 Isothermal and heated subsonic jet noise using large eddy simulations on unstructured grids. Comput. Fluids 171, 166192.
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Effects of nozzle-exit boundary-layer profile on the initial shear-layer instability, flow field and noise of subsonic jets

  • Christophe Bogey (a1) and Roberto Sabatini (a2)


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