Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-20T20:25:59.831Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of jet flow on jet noise via an extension to the Lighthill model

Published online by Cambridge University Press:  26 April 2006

Herbert S. Ribner
Herbert S. Ribner
Affiliation:
University of Toronto Institute for Aerospace Studies, Downsview M3H 5T6 CanadaandNASA Langley Research Center, Hampton, VA 23671-0001, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The Lighthill formalism for jet noise prediction is extended to accommodate wave transport by the mean jet flow. The extended theory combines the simplicity of the Lighthill approach with the generality of the more complex Lilley approach. There is full allowance for ‘flow-acoustic’ effects: shielding, as well as the refractive ‘cone of (relative) silence’. A source term expansion yielda a convected wave equation that retains the basic Lighthill source term. This leads to a general formula for power spectral density emitted from unit volume as the Lighthill-based value multiplied by a squared ‘normalized’ Green's function. The Green's function, referred to a stationary point source, delineates the refraction dominated ‘cone of silence’. The convective motion of the sources, with its powerful amplifying effect, also directional, is accounted for in the Lighthill factor. Source convection and wave convection are thereby decoupled, in contrast with the Lilley approach: this makes the physics more transparent. Moreover, the normalized Green's function appears to be near unity outside the ‘cone of silence’. This greatly reduces the labour of calculation: the relatively simple Lighthill-based prediction may be used beyond the cone, with extension inside via the Green's function. The function is obtained either experimentally (injected ‘point’ source) or numerically (computational aeroacoustics). Approximation by unity seems adequate except near the cone and except when there are coaxial or shrouding jets: in that case the difference from unity will quantify the shielding effect. Further extension yields dipole and monopole source terms (cf. Morfey, Mani, and others) when the mean flow possesses density gradients (e.g. hot jets).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 321 , 25 August 1996 , pp. 1 - 24
Copyright
© 1996 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahuja, K. K. 1972 An experimental study of subsonic jet noise with particular reference to the effect of upstream disturbances. MPhil. Thesis, University of London.
Atvars, J., Schubert, L. K., Grande, E. & Ribner, H. S. 1965 Refraction of sound by jet flow or jet temperature. University of Toronto Institute for Aerospace Studies, UTIAS TN 109, 1965; NASA CR-494, 1966.
Balsa, T. F. 1976a The far field of high frequency convected singularities in sheared flows, with an application to jet noise prediction. J. Fluid Mech. 74, 193–208.Google Scholar
Balsa, T. F. 1976b The shielding of a convected source by an annular jet with an application to the performance of multitude suppressors. J. Sound Vib. 44, 179–189.Google Scholar
Balsa, T. F. 1977 The acoustic field of source in shear flow with application to jet noise: convective amplification. J. Fluid Mech. 79, 33–47.Google Scholar
Balsa, T. F. & Gliebe, P. R. 1977 Aerodynamics and noise of coaxial jets. AIAA J. 15, 1550–1558.Google Scholar
Balsa, T. F., Gliebe, P. R., Kantola, R. A., Mani, R., Stringas, E. J. & Wang, J. C. F. 1978 High velocity jet noise source location and reduction. Task 2 — theoretical developments and basic experiments. FAA-RD76-79, II. (Available DTIC as AD A094291.)
Bayliss, A., Maestrello, L., McGreevy, J. L. & Fenno, C. C. 1995 Response of multi-panel assembly to noise from a jet in forward motion. 1st Joint CEAS/AIAA Aeroacoustics Conf. (16th AIAA Aeroacoustics Conf.), Munich, 12–15 June.
Blokhintsev, D. I. 1956 Acoustics of a nonhomogeneous moving medium. NACA TM 1399 (translation of ‘Akustika Neodnorodnoi Dvizhushcheisya Sredy’. Ogiz, Gosudarstvennoe Izdatel’ stvo, Tekhniko-Teoreticheskoi Literatury, Moskva, 1946, Leningrad).
Chu, W. T. 1966 Turbulence measurements relevant to jet noise. University of Toronto, Institute for Aerospace Studies, UTIAS Rep. 119.
Chu, W. T. 1973 Moving frame analysis of jet noise. J. Acoust. Soc. Am. 53, 1439–1440.Google Scholar
Chu, W. T. 1974 Narrow band measurements of jet noise carried out in the USC anechoic jet facility. Department of Aerospace Engineering, University of Southern California Report.
Csanady, G. T. 1966 The effect of mean velocity variations on jet noise. J. Fluid Mech. 26, 183–197.Google Scholar
Davies, P. O. A. L., Fisher, M. J. & Barratt, M. J. 1963 The characteristics of the turbulence in the mixing region of a round jet. J. Fluid Mech. 15, 337–367.Google Scholar
Doak, P. E. 1972 Analysis of internally generated sound in continuous materials: 2. A critical review of the conceptual adequacy and physical scope of existing theories of aerodynamic noise, with special reference to supersonic jet noise. J. Sound Vib. 25, 263–335.Google Scholar
Ffowcs Williams, J. E. 1960 Some thoughts on the effects of aircraft motion and eddy convection on the noise from air jets. University of Southampton, Department of Aeronautics and Astronautics, USAA Rep. 155.Google Scholar
Ffowcs Williams, J. E. 1963 The noise from turbulence convected at high speed. Phil. Trans. R. Soc. Lond. A 255, 469–503.Google Scholar
Gliebe, P. R. 1980 Diagnostic evaluation of jet noise suppression mechanisms. J. Aircraft 17, 837 842.Google Scholar
Gliebe, P. R. & Balsa, T. F. 1978 Aeroacoustics of axisymmetric single- and dual-flow exhaust nozzles. J. Aircraft 15, 743–749.Google Scholar
Gliebe, P. R., Brausch, J. F., Majjigi, R. K. & Lee, R. 1991 Jet noise suppression. Aeroacoustics of Flight Vehicles: Theory and Practice. Vol. 2: Noise Control. NASA Ref. Publication 1258, vol. 2; WRDC Tech. Rep. 90-3052, 207–269.Google Scholar
Goldstein, M. E. 1976 Aeroacoustics. McGraw-Hill.
Grande, E. 1966 Refraction of sound by jet flow and jet temperature II. University of Toronto Institute for Aerospace Studies, UTIAS TN 110, 1966; NASA CR-840, 1967.Google Scholar
Grosche, F.-R., Jones, J. H. & Wilhold, G. A. 1973 Measurements of the distribution of sound source intensities in turbulent jets. AIAA Aero-Acoustics Conf. Seattle, 15–17 October, paper 73 989.
Kraichnan, R. H. 1953 The scattering of sound in a turbulent medium. J. Acoust. Soc. Am. 25, 1096–1104.Google Scholar
Krishnappa, G. 1968 Estimation of the intensity of noise radiated from a subsonic circular jet. Proc. AFOSR/University of Toronto Institute for Aerospace Studies Symp. Toronto. University of Toronto Press.
Krishnappa, G. & Csanady, G. T. 1969 An experimental investigation of the composition of jet noise. J. Fluid Mech. 37, 149–159.Google Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically — I. General theory. Proc. R. Soc. Lond. A 211, 564–587.Google Scholar
Lighthill, M. J. 1954 On sound generated aerodynamically — II. Turbulence as a source of sound. Proc. R. Soc. Lond. A 222, 1–32.Google Scholar
Lighthill, M. J. 1953 On the energy scattered from the interaction of turbulence with sound or shock waves. Proc. Camb. Phil. Soc. 49, 531–551.Google Scholar
Lilley, G. M. 1958 On the noise from air jets. Aeronautical Research Council (Great Britain), ARC 20, 376-N40-FM2724.
Lilley, G. M. 1972 The generation and radiation of supersonic jet noise. Vol. IV-Theory of turbulence generated jet noise, noise generation from upstream sources, and combustion noise, Part II: Generation of sound in a mixing region. Air Force Aero Propulsion Lab., AFAPL-TR- 53.
Lush, P. A. 1971 Measurements of subsonic jet noise and comparison with experiment. J. Fluid Mech. 46, 477–500.Google Scholar
Maestrello, L. 1976 Two-point correlations of sound pressure in the far field of a jet: Experiment NASA TM X-72835.
Mani, R. 1972 A moving source problem relevant to jet noise. J. Sound Vib. 25, 337–347.Google Scholar
Mani, R. 1976a The influence of jet flow on jet noise. Part 1. The noise of unheated jets. J. Fluid Mech. 73, 753–778.Google Scholar
Mani, R. 1976b The influence of jet flow on jet noise. Part 2. The noise of heated jets. J. Fluid Mech. 73, 779–793.Google Scholar
Mawardi, O. K. 1955 On the spectrum of noise from turbulence. J. Acoust. Soc. Am. 27, 1995, pp. 442–445.Google Scholar
Michalke, A. & Michel, U. 1979 Prediction of jet noise in flight from static tests. J. Sound Vib. 67, 347–367.Google Scholar
Michalke, A. & Michel, U. 1980 Prediction of flyover noise from single and coannular jets. AIAA paper 80-1031.Google Scholar
Mollo-Christensen, E., Kolpin, M. A. & Martucelli, J. R. 1963 Experiments on jet flows and jet noise. Far field spectra and directivity patterns. MIT Aeroelasticity and Structures Research Laboratory, ASRL TR 1007.
Moon, L. F. & Zelazny, S. W. 1975 Experimental and analytical study of jet noise modeling. AIAA J. 13, 387–393.Google Scholar
Morfey, C. L. 1973 Amplification of aerodynamic noise by convected flow inhomogeneities. J. Sound Vib. 31, 391–397.Google Scholar
Morfey, C. L., Szewczyk, V. M. & Tester, B. J. 1978 New scaling laws for hot and cold jet mixing noise, based on a geometric acoustics model. J. Sound Vib. 61, 255–292.Google Scholar
Mungur, P., Plumblee, H. E. & Doak, P. E. 1974 Analysis of acoustic radiation in a jet flow environment. J. Sound Vib. 36, 21–52.Google Scholar
Musafir, R. E. 1986 The use of polar correlation in the characterization of multipolar source distributions. Analysis, Inter-noise 86, Cambridge, MA, 21–23 July, pp. 1335–1340.
Musafir, R. E., Slama, J. G. & Zindeluk, M. 1984 Quadrupole correlations and jet noise. Physical Phenomena, Inter-noise 84, Honolulu, 3–5 December, pp. 257–260.
Nossier, N. S. M. & Ribner, H. S. 1975 Tests of a theoretical model of jet noise. AIAA paper 75-436.Google Scholar
Pao, S. P. & Lowson, M. V. 1970 Some applications of jet noise theory. AIAA paper 70-233, January, New York.Google Scholar
Phillips, O. M. 1960 On the generation of sound by supersonic turbulent shear layers. J. Fluid Mech. 9, 1–28.Google Scholar
Powell, A. 1954 Survey of experiments on jet-noise. Aircraft Engng 26, 2–9.Google Scholar
Powell, A. 1960 Fundamental notions concerning convection of aerodynamic noise generators. Program, 59th mtg Acoust. Soc. Am. Providence, RI, 9–11 June, paper 05 (abstract).
Proudman, I. 1952 The generation of noise by isotropic turbulence. Proc. R. Soc. Land. A 214, 119–132.Google Scholar
Ribner, H. S. 1953 Convection of a pattern of vorticity through a shock wave. NACA TN 2864, 1953, NACA Rep. 1164, 1954.Google Scholar
Ribner, H. S. 1954 Shock-turbulence interaction and the generation of noise. NACA TN 3255, 1954, NACA Rep. 1233, 1955.Google Scholar
Ribner, H. S. 1960 Energy flux from an acoustic source contained in a moving fluid element and its relation to jet noise. J. Acoust. Soc. Am. 32, 1159–1160 (Letter).Google Scholar
Ribner, H. S. 1962 Aerodynamic sound from fluid dilatations: a theory of sound from jets and other flows. University of Toronto, Institute of Aerophysics (now Aerospace Studies), UTIA Rep. 86, AFOSR TN 3430.Google Scholar
Ribner, H. S. 1964 The generation of sound by turbulent jets. Advances in Applied Mechanics, vol. 8, pp. 103–182. Academic.
Ribner, H. S. 1969 Quadrupole correlations governing the pattern of jet noise. J. Fluid Mech. 38, 1–24.Google Scholar
Ribner, H. S. 1977 On the role of the shear term in jet noise. J. Sound Vib. 52, 121–132.Google Scholar
Ribner, H. S. 1978 Two point correlations of jet noise. J. Sound Vib. 56, 1–19.Google Scholar
Ribner, H. S. 1981 Perspectives on jet noise. Dryden Lecture. AIAA J. 19, 1513–1526.Google Scholar
Ribner, H. S. 1995 An extension of the Lighthill theory of jet noise to encompass refraction and shielding. NASA TM 110163.
Richarz, W. G. 1979 Theory of cross-spectral densities of jet noise. Mechanics of Sound Generation in Flows, IUTAM/ICA/AIAA Symp., Gottingen, Max-Planck-Institut fur Stromungsforschung, 28–31 August (ed. E. A. Muller), pp. 153–158.
Schubert, L. K. 1969 Refraction of sound by a jet: a numerical study. University of Toronto Institute for Aerospace Studies, Rep. 144.Google Scholar
Schubert, L. K. 1972a Numerical study of sound refraction by a jet flow I. Ray acoustics. J. Acoust. Soc. Am. 51, 439–446.Google Scholar
Schubert, L. K. 1972a Numerical study of sound refraction by a jet flow II. Wave acoustics. J. Acoust. Soc. Am. 51, 447–463.Google Scholar
Tam, C. K. W. 1991 Jet noise generated by large-scale coherent motion. Aeroacoustics of Flight Vehicles: Theory and Practice. Vol 1: Noise Sources. NASA Ref. Pub. 1258. vol. 1; WRDC Tech. Rep. 90-3052, 311–390.
Tester, B. J. & Morfey, C. L. 1976 Developments in jet noise modelling — theoretical predictions and comparison with measured data. J. Sound Vib. 46, 79–103.Google Scholar