Influence of Source Interference on the Directivity of Jet Mixing Noise.

Kurzfassung

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.