A complex-valued resonance model for axisymmetric screech tones in supersonic jets

TL;DR

This paper develops an advanced linear-stability-based resonance model incorporating finite shear-layer thickness and complex wave properties to predict and analyze screech tones in supersonic jets, aligning well with experimental data.

Contribution

It introduces a comprehensive resonance model with complex wavenumbers and frequencies, accounting for shear-layer effects and reflection coefficients, improving screech tone predictions.

Findings

The model accurately predicts screech frequencies across various conditions.

Finite shear-layer thickness significantly influences resonance behavior.

Reflection coefficients are crucial for modeling resonance loop amplification.

Abstract

We model the resonance mechanism underpinning generation of A1 and A2 screech tones in an under-expanded supersonic jet. Starting from the resonance model recently proposed by \cite{mancinelli2019screech}, where the upstream-travelling wave is a neutrally-stable guided jet mode, we here present a more complete linear-stability-based model for screech prediction. We study temperature and shear-layer thickness effects and show that, in order to accurately describe the experimental data, the effect of the finite thickness of the shear layer must be incorporated in the jet-dynamics model. We then present an improved resonance model for screech-frequency predictions in which both downstream- and upstream-travelling waves may have complex wavenumber and frequency. This resonance model requires knowledge of the reflection coefficients at the upstream and downstream locations of the resonance loop. We explore the effect of the reflection coefficients on the resonance model and propose an approach for their identification. The complex-mode model identifies limited regions of frequency-flow parameter space for which the resonance loop is amplified in time, a necessary condition for the resonance to be sustained. This model provides an improved description of the experimental measurements.