LEAKY WAVES AND THE PRODUCTION OF SOUND BY TURBULENT-FLOW FROM AN ELASTIC NOZZLE

An analysis is made of the sound generated by axisymmetric multipole s ource distributions interacting with the open end of a coaxial nozzle modeled by a semi-infinite circular elastic duct. The influence of sur face compliance is important at frequencies below the coincidence freq uency omega(c) of bending waves on a plate of the same thickness as th e duct wall. At frequencies between the ring frequency of the duct, om ega(R), and omega(c), the intensity of the sound scattered from the op en end is reduced relative to that produced by the same source when th e duct is rigid. At lower frequencies, scattering is dominated by soun d launched by leaky extensional waves of the duct, such that the inten sity of the radiation exceeds that from a rigid duct by a factor of or der 1/(kappa(0)a)(2) >> 1, where kappa(0) and a are, respectively, the acoustic wavenumber and duct radius. The leaky waves propagate supers onically relative to the fluid and cause the radiation directivity to be sharply peaked in an upstream direction determined by the ratio of the sound speed in the fluid and the leaky wave phase velocity. Applic ation of the theory is made to determine the axisymmetric component of the sound produced by low Mach number turbulent flow from the nozzle. Structural compliance would normally be expected to reduce the direct radiation produced by an adjacent turbulent flow, and this is confirm ed in the present case at source frequencies between omega(R) and omeg a(c). At lower frequencies, however, the effect is offset by the great er efficiency of leaky wave generation. The net result is that the ove rall acoustic spectral levels are similar to those for a rigid nozzle, but the directivity is significantly different. Subsonically propagat ing flexural waves are also generated at the nozzle with an efficiency which, in the case of a steel nozzle in water, exceeds that of sound production via the leaky waves by 30-40 dB at low frequencies. Their i nfluence in the fluid decays rapidly with distance from the nozzle axi s, but they may, in practice, make a significant contribution to the f low-generated sound if they are scattered at structural discontinuitie s upstream of the nozzle exit. The results are illustrated by numerica l predictions for a steel nozzle in water. An appendix contains a deri vation of a new formula for the sound power radiated by a leaky wave.