Sound generated by the interaction between shock and instability waves in supersonic round jets

TL;DR

This paper develops an analytical model for sound generated by shock-instability interactions in supersonic round jets, revealing key directivity features and the inadequacy of the monopole assumption, with results aligning well with experimental data.

Contribution

The study extends previous planar models to circular jets, providing a closed-form solution for the acoustic field and insights into shock-related noise mechanisms.

Findings

Sound directivity matches experimental screech patterns.

Noise intensity decays near 180-degree observer angle.

Mach wave radiation is the primary noise generation mechanism.

Abstract

In this paper, we develop an analytical model to investigate the sound generated by the shock-instability interactions (SII) in supersonic round jets, extending our previous two-dimensional planar study to circular configurations. The jet is represented by a vortex sheet, with its motion modeled by the Euler equations. Shock and instability waves are modeled using Pack's approach and the linear stability theory, respectively, while their interaction is calculated by solving an inhomogeneous wave equation. Using the Fourier transform and steepest descent method, we obtain a closed-form solution for the resulting acoustic field. Results due to the interaction between the instability waves and one interaction cell capture the key directivity features of screech reported in experiments and numerical simulations, indicating that the classic monopole assumption may be inadequate. In particular, the screech-tone intensity due to multiple shock cells decays rapidly as the observer angle approaches 180 degrees, which is in better agreement with the experimental data measured by Norum. We further analyze how the instability wave growth rate influences these directivity patterns and examine the sound generation efficiency of the broadband shock-associated noise. Finally, an examination of near-field pressure fluctuations due to the SII reveals that noise is produced primarily via the Mach wave radiation mechanism.