On the instabilities of intrinsic thermoacoustic modes in a thermoacoustic waveguide with anechoic terminations

TL;DR

This paper investigates the instabilities of intrinsic thermoacoustic modes in finite thermoacoustic waveguides with anechoic terminations, revealing how these modes evolve and affect sound control in practical devices.

Contribution

It uncovers and analyzes the occurrence of evanescent and intrinsic thermoacoustic modes in finite TAWGs, providing insights into their stability and implications for device design.

Findings

ITA modes are linked to acoustic-driven evanescent modes.

ITA modes become unstable as thermoacoustic coupling increases.

Stability analysis distinguishes between evanescent and intrinsic modes.

Abstract

A recent study [H. Hao and F. Semperlotti, Phys. Rev. B 104, 104303 (2021)] investigated the dynamic behavior of an infinite one-dimensional (1D) thermoacoustic waveguide (TAWG) and illustrated its ability to sustain nonreciprocal and near zero-index sound propagation behavior; these properties can be very beneficial in the design of acoustic devices, including acoustic diodes, amplifiers, and cloaks. Nevertheless, it is critical to realize that when this concept is implemented in a finite-length waveguide, dynamic instabilities may occur and either drastically reduce or completely hinder the ability of the TAWG to control and manipulate sound. In this work, we uncover and investigate the occurrence of either evanescent or intrinsic thermoacoustic (ITA) modes in a 1D TAWG with anechoic terminations. The stability analysis clearly distinguishes these two types of evanescent modes and highlights their different origin rooted in either acoustic or thermoviscous effects. Numerical results reveal that ITA modes in anechoic-terminated TAWG are strictly connected to the acoustic-driven evanescent modes, and evolve towards unstable modes as the TA coupling strength is increased. This study may have important implications for the practical design of novel acoustic manipulating devices enabled by TA coupling elements. The conclusions drawn in this study may also shed lights on the effective suppression of instabilities in TAWGs.