Influence of Source Interference on the Directivity of Jet Mixing Noise

A simple model is proposed for the description of the interference effects on the radiation of jet mixing noise. It is used to show analytically that many experimental observations in the acoustic far field of a jet can be explained with the acoustic analogy. This relates not only to the directivity of a static jet as was already shown by Lighthill, but also to the unexpectedly high noise radiation into the forward arc in flight. It also explains the experimental evidence that the peak frequency of a static jet is almost constant over a wide range of emission angles for a static jet and is subject to a Doppler frequency shift in flight. It is necessary to describe the turbulent flow quantities in the coordinate system fixed on the nozzle, in which the source quantities are stationary random and the limits of the source integral are stationary. An integral for the power-spectral density is derived, which includes the quadrupole and the dipole sources. Turbulence convection is considered through a phase angle of the cross-spectral density of the sources. The influence of source interference is expressed in terms of an interference integral which describes the sound radiation of one source volume element. In order to achieve analytic solutions for this integral, the radial extension of the jet is neglected and simple models are introduced for the decay of the coherence with increasing axial separation of the source positions. The decay is shown to have a large influence on the radiation, especially into the forward arc.

[1]  A. Michalke,et al.  Some remarks on source coherence affecting jet noise , 1983 .

[2]  H. S. Ribner,et al.  New Theory of Jet‐Noise Generation, Directionality, and Spectra , 1959 .

[3]  Gunter Hermann,et al.  On the inviscid instability of a circular jet with external flow , 1982, Journal of Fluid Mechanics.

[4]  Ulf Michel,et al.  Prediction of Flyover Jet Noise Spectra , 1981 .

[5]  W. Möhring,et al.  On vortex sound at low Mach number , 1978, Journal of Fluid Mechanics.

[6]  J. E. Ffowcs Williams.  The noise from turbulence convected at high speed , 1963, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[7]  A. Michalke,et al.  On the effect of spatial source coherence on the radiation of jet noise , 1977 .

[8]  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.

[9]  U. Michel.  Broadband Shock Noise: Theory vis-a-vis Experimental Results. , 1995 .

[10]  C. Morfey.  Amplification of aerodynamic noise by convected flow inhomogeneities , 1973 .

[11]  H. S. Ribner,et al.  Refraction of sound by jet flow or jet temperature , 1965 .

[12]  H. S. Ribner,et al.  Refraction of Sound from a Point Source Placed in an Air Jet , 1965 .

[13]  Christopher K. W. Tam,et al.  COMPUTATIONAL AEROACOUSTICS EXAMPLES SHOWING THE FAILURE OF THE ACOUSTIC ANALOGY THEORY TO IDENTIFY THE CORRECT NOISE SOURCES , 2002 .

[14]  A. Michalke,et al.  An Expansion Scheme for the Noise from Circular Jets , 1971 .

[15]  C. Tam,et al.  Jet Mixing Noise from Fine-Scale Turbulence , 1998 .

[16]  A. Powell.  Theory of Vortex Sound , 1964 .

[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]  H. Ribner.  Aerodynamic sound from fluid dilitations; a theory of the sound from jets and other flows , 1962 .

[19]  A. Michalke,et al.  A Wave model for Sound Generation in Circular Jets , 1970 .

[20]  J. S. Wang.  Statistical Theory of Superlattices with Long-Range Interaction. I. General Theory , 1938 .

[21]  L. Maestrello,et al.  Statistical properties of the sound and source fields of an axisymmetric jet , 1977 .

[22]  Ulf Michel,et al.  Prediction of Flyover Jet Noise Spectra from static Tests , 1980 .

[23]  Ulf Michel,et al.  Prediction of jet noise in flight from static tests , 1979 .