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.

Experimental characterisation of the screech feedback loop in underexpanded round jets

“…They observed that the passage of an eddy at a shock position may cause the shock to leak out from the mixing layer. Shariff & Manning (2013) observed the same phenomenon from a ray tracing study. Shock leakage has also been recognised as being the screech acoustic feedback generation mechanism by Berland, Bogey & Bailly (2007) by means of a large-eddy simulation of a planar jet.…”

A schlieren and nearfield acoustic based experimental investigation of screech noise sources

“…A second criterion to select the feedback source is to account only for those located at a shock tip. This is the most probable location according to numerical studies of shock leakage by Suzuki et al, 8 Shariff and Manning, 9 or Berland et al 10 It is shown that a moving shock is a source of compression and expansion waves that are normally internally reflected, but that can leak if some requirements on the vorticity in the shear layer are met, especially for large vortical structures, thus if coherent structures are developed enough. This analysis will assume the speed of sound constant while traveling in the jet vicinity, and there is no account for non-linear effects.…”

Modulation of downstream-propagating waves in aeroacoustic resonance

“…Shock-containing free shear flows frequently exhibit some form of aeroacoustic resonance, the most well known of these resonant processes are those that produce screech or impingement tones. 1 These resonance processes can be divided into four discrete processes: a downstream-propagating wave, 2-4 a tonal generation mechanism, [5][6][7][8][9] an upstream-propagating wave, [10][11][12][13][14][15] and a receptivity mechanism. [16][17][18] Of these, the downstream-propagating wave is the only process where energy is provided to the resonance loop; 2 the growth of the instability wave is driven by the extraction of energy from the mean flow.…”