ERCOFTAC Bulletin - Centre Acoustique

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for 0.3 ≤ St ≤ 0.5. Results are shown in Figure (7), taken from [5], and are compared to the axisymmetric mode of the pressure for the same frequency range. The agreement found at low angles (high x1 in Figure (7)) between the models with “unsteady envelope”, i.e. when temporal changes of A and L follow the simulation data, is reasonable for both computations. (a) SPL (dB) (b) SPL (dB) 125 120 115 110 105 100 95 90 DNS Steady envelope Unsteady envelope (analytical) Unsteady envelope (numerical) 85 0 2 4 6 8 10 12 14 125 120 115 110 105 100 95 90 x1/D LES Steady envelope Unsteady envelope (analytical) Unsteady envelope (numerical) 85 2 4 6 8 10 12 14 16 18 20 x1/D Figure 7: Comparison between jittering wave-packet models and numerical data of Mach 0.9 jets: (a) DNS (Freund[14]) and (b) LES (Daviller[12]). SPL taken for the axisymmetric mode of the acoustic pressure for 0.3 ≤ St ≤ 0.5. Taken from [5]. 6 Conclusions The results reviewed in the present paper show that the sound field at low axial angles from subsonic jets can be calculated using source models consisting of a train of axisymmetric structures that undergo an amplitude modulation. This has been accomplished both using experimental data, for which the source is modelled as linear instability waves, or numerical simulations that allow the use of full volume data for the velocity field. The current progress in both numerical simulations and measurement techniques can guide us further into the nature of the low azimuthal modes in free jets. Although a detailed characterisation of the full turbulent field seems to be a hard task, focus on the axisymmetric and on other low azimuthal modes allows considerable simplifications. Such modes have a relatively low energy level if compared to the overall turbulent fluctuations[30], but their higher acoustic efficiency can lead to significant sound radiation. The present work was supported by CNPq, National Council of Scientific and Technological Development – Brazil. The authors thank Daniel Rodríguez and Tim Colonius for the helpful discussions and for the PSE calculations. References [1] G. K. Batchelor and A. E. Gill. Analysis of the stability of axisymmetric jets. Journal of Fluid Mechanics, 14(04):529–551, 1962. [2] C. Brown and J. Bridges. Acoustic efficiency of azimuthal modes in jet noise using chevron nozzles. Technical report, National Aeronautics and Space Administration, 2006. [3] G. L. Brown and A. Roshko. On density effects and large structure in turbulent mixing layers. Journal of Fluid Mechanics, 64(4):775–816, 1974. [4] G. Broze and F. Hussain. Nonlinear dynamics of forced transitional jets: periodic and chaotic attractors. Journal of Fluid Mechanics, 263:93–132, 1994. [5] A. V. G. Cavalieri, P. Jordan, A. Agarwal, and Y. Gervais. Jittering wave-packet models for subsonic jet noise. Journal of Sound and Vibration, 330(18-19):4474–4492, 2011. [6] A. V. G. Cavalieri, P. Jordan, T. Colonius, and Y. Gervais. Axisymmetric superdirectivity in subsonic jets. In 17th AIAA/CEAS Aeroacoustics Conference and Exhibit, Portland, OR, USA, June 5-8 2011. [7] D. G. Crighton. Basic principles of aerodynamic noise generation. Progress in Aerospace Sciences, 16(1):31–96, 1975. [8] D. G. Crighton and M. Gaster. Stability of slowly diverging jet flow. Journal of Fluid Mechanics, 77(2):397–413, 1976. [9] D. G. Crighton and P. Huerre. Shear-layer pressure fluctuations and superdirective acoustic sources. Journal of Fluid Mechanics, 220:355–368, 1990. [10] S. C. Crow. Acoustic gain of a turbulent jet. In Phys. Soc. Meeting, Univ. Colorado, Boulder, paper IE, volume 6, 1972. [11] S. C. Crow and F. H. Champagne. Orderly structure in jet turbulence. Journal of Fluid Mechanics, 48(3):547–591, 1971. [12] G. Daviller. Etude numérique des effets de temperature dans les jets simples et coaxiaux. PhD thesis, Ecole Nationale Supérieure de Mécanique et d’Aérotechnique, Poitiers, France (in French), 2010. [13] J. E. Ffowcs Williams and A. J. Kempton. The noise from the large-scale structure of a jet. Journal of Fluid Mechanics, 84(4):673–694, 1978. [14] J. B. Freund. Noise sources in a low-Reynoldsnumber turbulent jet at Mach 0.9. Journal of Fluid Mechanics, 438:277–305, 2001. 38 ERCOFTAC Bulletin 90
[15] H. V. Fuchs and U. Michel. Experimental evidence of turbulent source coherence affecting jet noise. AIAA J, 16(9):871–872, 1978. [16] K. Gudmundsson and T. Colonius. Instability wave models for the near-field fluctuations of turbulent jets. Journal of Fluid Mechanics, 689:97–128, 2011. [17] T. Herbert. Parabolized stability equations. Annual Review of Fluid Mechanics, 29(1):245–283, 1997. [18] J. I. Hileman, B. S. Thurow, E. J. Caraballo, and M. Samimy. Large-scale structure evolution and sound emission in high-speed jets: real-time visualization with simultaneous acoustic measurements. Journal of Fluid Mechanics, 544:277–307, 2005. [19] A. K. M. F. Hussain and K. B. M. Q. Zaman. The ‘preferred mode’ of the axisymmetric jet. Journal of Fluid Mechanics, 110:39–71, 1981. [20] D. Juvé, M. Sunyach, and G. Comte-Bellot. Filtered azimuthal correlations in the acoustic far field of a subsonic jet. AIAA Journal, 17:112, 1979. [21] D. Juvé, M. Sunyach, and G. Comte-Bellot. Intermittency of the noise emission in subsonic cold jets. Journal of Sound and Vibration, 71:319–332, 1980. [22] M Kœnig, A. V. G. Cavalieri, P. Jordan, and Y. Gervais. Intermittency of the azimuthal components of the sound radiated by subsonic jets. In 17th AIAA/CEAS Aeroacoustics Conference and Exhibit, Portland, OR, USA, June 5-8 2011. [23] M. Kœnig, A. V. G. Cavalieri, P. Jordan, Y. Gervais, and D. Papamoschou. Far-field filtering for the study of jet noise: Mach and temperature effects. In 17th AIAA/CEAS Aeroacoustics Conference and Exhibit, Portland, OR, USA, June 5-8 2011. [24] H. K. Lee and H. S. Ribner. Direct correlation of noise and flow of a jet. The Journal of the Acoustical Society of America, 52:1280, 1972. [25] M. J. Lighthill. On sound generated aerodynamically. I. General theory. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, pages 564–587, 1952. [26] R. Mankbadi and J. T. C. Liu. Sound generated aerodynamically revisited: large-scale structures in a turbulent jet as a source of sound. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 311(1516):183–217, 1984. [27] A. Michalke. A wave model for sound generation in circular jets. Technical report, Deutsche Luft- und Raumfahrt, November 1970. [28] A. Michalke. Instabilitat eines Kompressiblen Runden Freistrahls unter Berucksichtigung des Einflusses der Strahlgrenzschichtdicke. Z. Flugwiss, 19:319–328; English translation: NASA TM 75190, 1977, 1971. [29] A. Michalke. Survey on jet instability theory. Progress in Aerospace Sciences, 21:159–199, 1984. [30] A. Michalke and H. V. Fuchs. On turbulence and noise of an axisymmetric shear flow. Journal of Fluid Mechanics, 70:179–205, 1975. [31] E. Mollo-Christensen. 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). Journal of Applied Mechanics, 34:1–7, 1967. [32] I. Proudman. The generation of noise by isotropic turbulence. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 214(1116):119–132, 1952. [33] D. Rodríguez, A. Samanta, A. V. G. Cavalieri, T. Colonius, and P. Jordan. Parabolized stability equation models for predicting large-scale mixing noise of turbulent round jets. In 17th AIAA/CEAS Aeroacoustics Conference and Exhibit, Portland, OR, USA, June 5-8 2011. [34] N. D. Sandham and A. M. Salgado. Nonlinear interaction model of subsonic jet noise. Philosophical Transactions of the Royal Society A, 366(1876):2745–2760, 2008. [35] T. Suzuki and T. Colonius. Instability waves in a subsonic round jet detected using a near-field phased microphone array. Journal of Fluid Mechanics, 565:197–226, 2006. [36] C. K. W. Tam and D. E. Burton. Sound generated by instability waves of supersonic flows. Part 2. Axisymmetric jets. Journal of Fluid Mechanics, 138(-1):273–295, 1984. [37] C. E. Tinney and P. Jordan. The near pressure field of co-axial subsonic jets. Journal of Fluid Mechanics, 611:175–204, 2008. ERCOFTAC Bulletin 90 39
Page 1 and 2: E R C O F T A C ERCOFTAC Bulletin M
Page 3 and 4: ERCOFTAC Bulletin 90, March 2012 TA
Page 5 and 6: Special Issue Coordinated by SIG-39
Page 7 and 8: serrations to full size wind-turbin
Page 9 and 10: Figure 5: Cross correlation of surf
Page 11 and 12: [11] Desqesnes, G., Terracol, M., a
Page 13 and 14: (a) (b) SPL (dB/Hz) SPL (dB/Hz) 90
Page 15 and 16: (a) (b) λ p /D λ p /D 1 0.8 0.6 0
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Page 19 and 20: via empirical mixing rules [17, 18,
Page 21 and 22: OASPL (dB) × × × × × × 10dB
Page 23 and 24: Numerical and Experimental Characte
Page 25 and 26: Figure 3: Views of the NACRE experi
Page 27 and 28: Figure 5: From top to bottom: (1) g
Page 29 and 30: case of the scarfed nozzle an almos
Page 31 and 32: marks indicate, that the scheme doe
Page 33 and 34: 2.8 Filtering The acoustic sources
Page 35 and 36: [5] D. P. Lockard and M. M. Choudha
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Page 39: The results of Figure (5) show a re
Page 43 and 44: and potential fatigue. However, the
Page 45 and 46: count are frequently made. However,
Page 47 and 48: Analytical and Numerical Wxtensions
Page 49 and 50: (y − y0) ≈ y becomes acceptable
Page 51 and 52: [15] M. A. Mac Donald, Y. Nishi, an
Page 53 and 54: 1. Large Eddy Simulation Geurts, B.
Page 55: The simultaneous presence of severa

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