A criterion for thermo-acoustic stability based on the flux of acoustic energy

Abstract

This paper introduces a conservative criterion for thermo-acoustic stability. By subdividing a thermo-acoustic system into a passive subsystem – containing no source of acoustic energy – and an active subsystem containing all sources, the criterion can be formulated as follows: For positive or zero growth rates, the passive subsystem cannot feed acoustic energy into the active part. If for a given frequency, the active subsystem absorbs acoustic energy at the interface, this stands in contradiction to the property of the passive subsystem to never feed into the active subsystem. Therefore the overall system cannot be unstable at that frequency. This holds without regard to the exact properties of the passive subsystem. This stability criterion may be regarded as a special case of the Acoustic Energy Dissipation/Production Potentiality introduced by Auregan and Starobinski (Acta Acustica united with Acustica 85 (6) 1999). Merely evaluating this criterion for all real-valued frequencies is insufficient. Instead, it is necessary to cover all positive growth rates, too. Finally, the present paper specifies an algorithm that avoids missing any instabilities in the (2D) complex plane, but allows the investigation of a 1D domain.