Abstract
Aweakdiscretization in the frequency domain of theLilley–Goldstein acoustic analogy equation is presented. This equation is cast into a linear system of two equations that are successively arranged in a convenient form for a Galerkin projection. The method is applied to compute the sound generated by Dirac ring sources of different azimuthal order and radius and propagated through an axisymmetric parallel jet. The effects due to the jet temperature and velocity profile combined with the effects due to the source frequency, radius, and azimuthal order are illustrated through extensive parametric results. It is shown that three-dimensional Green’s functions can be reconstructed by superposition of few axisymmetric solutions of low azimuthal order when the sources are located inside the jet. Finally, tones from annular sources located in the potential core of amixing jet are propagated through the jet shear layer and compared with the tones computed in uniform flow conditions. It is shown that, for conditions that are representative of a propeller rig located in the potential core of a wind-tunnel jet, the shear-layer refraction effects can be corrected by using a thin-layer approximation.
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