Acoustic reflection of vorticity waves at a shrouded-jet exit in ``howling" resonances

Abstract

At some operating conditions shrouded jets are observed to undergo an intense howling resonance. The coupling of vortical modes in the jet with acoustic modes at the shroud exit, which potentially close the resonance loop, are investigated with a vortex sheet model, which is solved using scalar Wiener-Hopf techniques. Peculiar sensitivities to flow parameters are observed that might explain the sporadic character of the observed howling resonance. So-called howling resonances have been observed in several shrouded jets, 1–4 all sharing the basic configuration shown in figure 1. Shocks cells in the jet are thought to sometimes play a role, 5 but for subsonic jets the mechanism is expected to involve interaction with the jet and its shroud. 1 To close a resonance, vortical jet structures must couple with the acoustic modes of the shroud. The most likely place for this to occur is at the exit, which is the focus of our investigation. We consider a semi-infinite cylindrical shroud with a co-flowing inner jet issuing out of it. The uniform inner, outer and ambient flows are separated by vortex sheets, with the outer vortex sheet originating at the shroud exit. A scalar Wiener–Hopf method is used to calculate how vorticity waves on the inner shear layer scatter at the shroud exit into reflected upstream propagating acoustic waves. The interaction of interest is fundamentally finite wavelength and apparently asymmetric, so high- or low-frequency approximations can not be made to simplify the analysis. This finite-wavelengths analysis builds upon an existing theoretical framework for edge scattering problems. 6–11