Exceptional points in the thermoacoustic spectrum

TL;DR

This paper identifies and analyzes exceptional points in the spectrum of a thermoacoustic system, revealing critical sensitivities and mode interactions that impact physical understanding and control strategies.

Contribution

It demonstrates the presence of exceptional points in thermoacoustic spectra and explores their implications for system sensitivity and mode behavior.

Findings

Exceptional points cause eigenvalue and eigenfunction coalescence.

Sensitivity of the system becomes infinite at exceptional points.

Interaction between acoustic and thermoacoustic modes is characterized.

Abstract

Exceptional points are found in the spectrum of a prototypical thermoacoustic system as the parameters of the flame transfer function are varied. At these points, two eigenvalues and the associated eigenfunctions coalesce. The system's sensitivity to changes in the parameters becomes infinite. Two eigenvalue branches collide at the exceptional point as the interaction index is increased. One branch originates from a purely acoustic mode, whereas the other branch originates from an intrinsic thermoacoustic mode. The existence of exceptional points in thermoacoustic systems has implications for physical understanding, computing, modeling and control.