Reflection and transmission of a Kelvin-Helmholtz wave incident on a shock in a jet

TL;DR

This paper investigates how Kelvin-Helmholtz waves interact with shocks in jets, focusing on wave reflection and transmission, to improve understanding of jet resonance phenomena and acoustic feedback mechanisms.

Contribution

It introduces a mode-matching approach to analyze wave reflection and transmission at shocks, considering both vortex-sheet and finite-thickness shear-layer models, addressing missing physics in existing resonance models.

Findings

Quantified the impact of shear layer thickness on wave reflection.

Demonstrated the mode-matching approach's effectiveness in predicting wave behavior.

Provided insights into wave interactions that influence jet screech tones.

Abstract

Screech tones in supersonic jets are underpinned by resonance between downstream-travelling Kelvin-Helmholtz waves and upstream-travelling acoustic waves. Specifically, recent work suggests that the relevant acoustic waves are guided within the jet and are described by a discrete mode of the linearised Navier-Stokes equations. However, the reflection mechanism that converts downstream-travelling waves into upstream-travelling waves, and vice versa, has not been thoroughly addressed, leading to missing physics within most resonance models. In this work we investigate the reflection and transmission of waves generated by the interaction between a Kelvin-Helmholtz wave and a normal shock in an under-expanded jet using a mode-matching approach. Both vortex-sheet and finite-thickness shear-layer models are explored, quantifying the impact of the shear layer in the reflection process. This approach could enable more quantitative predictions of resonance phenomena in jets and other fluid systems.