  The onset of thermoacoustic instabilities in lean-premixed gas-turbine
combustors is a crucial problem leading to degradation in engine and emissions
performance and shortened component life. The main aim of this study is to
propose a methodology based both on concepts of nonlinear dynamics and on
geometric-topological invariants, for the characterization of attractors
related to measurements based on the flame spontaneous light emission, like OH*
radical, in order to classify different phases of the combustion process and to
better recognize the transition mechanisms leading to the thermoacoustic
instabilities. Preliminary results, clearly show the powerfulness of the
approach to show the dynamical evolution of the flame and to evidence the onset
of the thermoacoustic instabilities: in particular the topological invariant
index (genus and related quantities) appear s as the best candidate for an
early indicator of the dynamical transition, characterized by the onset of a
more persistent, low entropy torus (quasi-periodic motion), as the related
thermoacoustic attractor.
