Adjoint-based linear analysis in reduced-order thermo-acoustic models

TL;DR

This paper develops the linear adjoint theory for thermo-acoustic systems, enabling sensitivity analysis and design optimization, demonstrated through applications to a damped oscillator and a heated Rijke tube.

Contribution

It provides a mathematical foundation for adjoint-based sensitivity analysis in thermo-acoustics, extending previous work and applying it to complex systems with mean-flow discontinuities.

Findings

Passive device effects on system stability identified

Mean-flow temperature discontinuity impacts sensitivity results

Analytical and numerical solutions validate the adjoint approach

Abstract

This paper presents the linear theory of adjoint equations as applied to thermo-acoustics. The purpose is to describe the mathematical foundations of adjoint equations for linear sensitivity analysis of thermo-acoustic systems, recently developed by Magri and Juniper (J. Fluid Mech. (2013), vol. 719, pp. 183--202). This method is applied pedagogically to a damped oscillator, for which analytical solutions are available, and then for an electrically heated Rijke tube with a mean-flow temperature discontinuity induced by the compact heat source. Passive devices that most affect the growth rate / frequency of the electrical Rijke-tube system are presented, including a discussion about the effect of modelling the mean-flow temperature discontinuity.