The spectral broadening of sound by turbulent shear layers. Part 2. The spectral broadening of sound and aircraft noise

It has been observed experimentally by Candel, Julienne & Julliand (1975) that a monochromatic test tone generated by a source inside a jet is received outside as a broad frequency band of definite shape. This phenomenon of spectral broadening occurs during transmission through the shear layer, which generally has a randomly irregular and unsteady shape, contains in addition distributed turbulence, and separates the jet and the ambient medium. We show in the first place that, in the audible range of frequencies, neither the approximation which treats the shear layer as a scattering interface with a convected undulating shape nor the opposite, high frequency limit obtained by means of asymptotic estimation of integrals derived for the diffraction of rays in turbulence is sufficient to provide a satisfactory theory of the observations. The refraction integrals obtained in part 1 have to be evaluated exactly in order to account for the phenomenon of spectral broadening, the methods used possibly being of interest in other branches of wave theory. The formation of the transmitted spectrum from an incident tone can be illustrated by representing a simple shear layer as an array of elements each re-radiating energy received from the source with its own characteristic attenuation and frequency shift. A computer program is used to obtain spectra under conditions corresponding to the experiments of Candel, Guedel & Julienne (1975) and gives encouraging agreement with their measurements, which were made with high frequency sources immersed in low speed jets. The theory can also be applied to the prediction of spectra received at various angles to the axis of high subsonic jets, but depends on extrapolation when supersonic exhausts are considered. We conclude with an example of the possible relevance of spectral broadening as a means of reducing the noise disturbance from current jet-powered aircraft, such as Concorde.

[1]  J. D. Morgan,et al.  A linear model of a finite amplitude Helmholtz instability , 1974, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[2]  M. Lighthill,et al.  The Bakerian Lecture, 1961 Sound generated aerodynamically , 1962, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[3]  M. Lighthill.  On sound generated aerodynamically II. Turbulence as a source of sound , 1954, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[4]  L. M. B. C. Campos.  On the emission of sound by an ionized inhomogeneity , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[5]  L. M. B. C. Campos.  The spectral broadening of sound by turbulent shear layers. Part 1. The transmission of sound through turbulent shear layers , 1978 .

[6]  Luís Campos.  On the generation and radiation of magneto-acoustic waves , 1977, Journal of Fluid Mechanics.

[7]  Refraction and shielding of sound from a source in a jet , 1976 .

[8]  J. Hammersley,et al.  Monte Carlo Methods , 1965 .

[9]  O. M. Phillips,et al.  On the generation of sound by supersonic turbulent shear layers , 1960, Journal of Fluid Mechanics.

[10]  Application of energy conservation to the solution of radiation problems involving uniformly convected source distributions , 1975 .

[11]  P. Beckmann,et al.  The scattering of electromagnetic waves from rough surfaces , 1963 .

[12]  M. Skolnik,et al.  Introduction to Radar Systems , 2021, Advances in Adaptive Radar Detection and Range Estimation.

[13]  Michael Fisher,et al.  The characteristics of the turbulence in the mixing region of a round jet , 1963, Journal of Fluid Mechanics.

[14]  L. Rayleigh.  XXXI. On the widening of spectrum lines , 1915 .

[15]  J. Williams.  Sound production at the edge of a steady flow , 1974, Journal of Fluid Mechanics.

[16]  Rayleigh Lord,et al.  XXXV. On the limit to interference when light is radiated from moving molecules , 1889 .

[17]  M. Lighthill.  On sound generated aerodynamically I. General theory , 1952, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[18]  T. Balsa,et al.  The far field of high frequency convected singularities in sheared flows, with an application to jet-noise prediction , 1976, Journal of Fluid Mechanics.

[19]  M. Berry.  The statistical properties of echoes diffracted from rough surfaces , 1973, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[20]  Richard A. Silverman,et al.  Wave Propagation in a Random Medium , 1960 .