A ray tracing study of shock leakage in a model supersonic jet

Abstract

Recent work has described screech noise from a supersonic jet as being due to leakage of a wave that is otherwise trapped in the jet's interior. In that work, the simplest of many techniques used is ray tracing for a single shear-layer modeled as a row of Stuart vortices. In the present work, a lower row of vortices is added to form a plane jet. Instead of plotting ray paths, a technique of visualization analogous to streaklines is used that better corresponds to instantaneous density fields as observed, for instance, by the Schlieren method. This produces striking images that show leakage of waves at each internal reflection resulting in a row of acoustic sources as envisioned since the 1950s. However, the sources are not isotropic and each has a zone of silence in the downstream direction. Leakage creates a fold in the wave pattern internal to the jet which leads to fine scale features. Reported experiments have also observed fine scale features (described as splitting) in the shock-cell pattern; they may be related to those observed here. Internally reflected rays also undergo a diffusive process as they propagate down the jet. In particular, each successive internal reflection at an unsteady shear-layer scatters rays along a wider range of wave angle and makes them more susceptible to leakage at the next reflection. It also causes more downstream directivity for the more downstream sources. An important result is that as the Mach number Mj is varied, maxima in leakage rate and mean acoustic amplitude occur at (near) resonances between the Mach-wave and shear-layer periods. Maxima in sound pressure level versus Mj have also been reported for laboratory round jets. Finally, as the shear-layer thickness is increased, a minimum in the rate of leakage (correlated with a minimum in radiation amplitude) occurs due to the competing effects of increased shear-layer penetration versus reduced eddy passage frequency.