A systems view on non-normal transient growth in thermoacoustics

The present thesis investigates the non-normal dynamics of a simple thermoacoustic system. Such a system is modeled in a systems framework and viewed and treated as a collection of subsystems that are in continuous feedback. The systems framework proves to be a robust and holistic approach, bringing along a beneficially fresh and clear perspective on thermoacoustics. Sophisticated low-order models for the subsystems heat source and acoustics are derived and analyzed. The heat source is modeled using a filter-based representation with distributed time lag characteristics stemming from experimental or numerical data or semi-analytical approaches. The 1-D homentropic acoustic field incorporates mean flow effects and varying mean quantities. It is numerically approximated by a method of weighted residuals (Galerkin method), which exhibits very little spurious non-normality. It is argued that the output energy of a thermoacoustic system is a matter of choice that merely prescribes the perspective from which the observed dynamics need to be interpreted. Spurious non-normality originating from ill-conditioned discretized operators or from model limitations is contrasted to physical non-normality. The dynamics and mechanisms of physical optimal non-normal transient growth are investigated and explained from an energy flux- and source-based perspective. The occurrence of optimal non-normal transient growth around a stable fix point is shown to be highly improbable. Despite the possibility of encountering suboptimal non-normal transient growth, its magnitude is small and may not play an important role in the process of triggering a linearly stable thermoacoustic system towards a nonlinear oscillating state.