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Consequences of non-normality and nonlinearity in flow / premixed flame / acoustic interactions for combustion instability

Subject Area Fluid Mechanics
Term from 2011 to 2014
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 196670088
 
Final Report Year 2014

Final Report Abstract

Thermoacoustic systems such as jet engines or gas turbines for power generation are prone to self-excited, high-amplitude oscillations, leading to material fatigue or structural damage. This is particularly true when performing at a “green”, i.e. low-emission, operating point. For a linearly stable non-normal system, oscillation amplitudes may grow temporarily before eventually decaying. If this so-called transient growth leads to amplitudes sufficiently high to trigger nonlinear effects, the system may evolve towards an oscillating state at high amplitudes. The concepts of non-normality and nonlinearity were first established in the field of hydrodynamics, where they offered an explanation for bypass-transition to turbulence. At the start of the present project, only highly idealized model problems had been studied under the aspect of transient growth and nonlinear triggering in the field of thermoacoustics. The goal was thus to provide tools for the analysis of non-normal effects in systems of more applied interest such as premixed flames. Non-normal transient growth is investigated in thermoacoustic systems with simple 1D geometries, where mean flow effects are trivial and where the acoustic field is dominated by planar waves. The low-order models describing the premixed flame (i.e. G-Equation) and the acoustic field (i.e. including mean temperature gradients and flow) are rich representations of the respective dynamics. One of the key findings with respect to non-normal dynamics is that non-normal transient growth around a stable fix point – although existent and theoretically sound – is not a threat for triggering in such thermoacoustic systems. For these simple systems, the magnitude of non-normal transient growth is small and does not suffice to trigger nonlinearities. Also, it occurs only over short periods of time. The above observations hold independent of the energy norm used to quantify non-normal transient growth. It is shown that the energy metric merely prescribes the perspective from which non-normal transient growth needs to be interpreted. An additional, yet unexpected finding was the existence of an intrinsic thermoacoustic feedback loop. The intrinsic feedback loop may cause instability in an anechoic environment, where all sound waves generated by the flame are radiated away, which is contradictory to established thinking that thermoacoustic instability requires feedback with the global acoustic field. The most important outcome of the present study is that adopting a systems framework to describe thermoacoustics is a promising approach. The systems approach is a robust and rigorous platform, where insights from different fields of research can be consistently combined using a “common language”. It offers a large set of tools that are well established and readily available. Its main benefit, however, is that it offers a holistic view which provides the basis for a more general and fresh understanding of thermoacoustic dynamics. The models developed and analyzed in this project, as well as phenomena such as internal thermoacoustic feedback, were found by adopting a systemic perspective. These insights have spawned fresh impulses to thermoacoustic research. The discovery of internal thermoacoustic feedback is yet a matter of fruitful discussion.

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