The characterization of unstable combustion regimes is often performed in the light of the Rayleigh Criterion, in the frequency domain, employing the Power Spectral Analysis of pressure (p′) and heat-release (q′) fluctuations. Equally often, it is assumed a priori that the thermo-acoustic oscillations are periodic, with a dominant frequency and a fixed amplitude (Period-1Llimit Cycle Oscillations). However one has to consider that: 1) p′ and q′, involved in the Rayleigh instability index, are governed by the Linearized Acoustic Energy Perturbation Balance Equations; 2) in the frequency domain any interdependence is measured by the coherence function, based on cross spectral densities, or Fourier spectra of cross-correlations, that in turn suppose a linear interdependence between sampled quantities. Conversely, recent experiments reveal that even simple thermo-acoustic systems exhibit nonlinear behaviour, far more elaborate than period-1 limit cycle oscillations. Therefore, in addition to the conventional linear analysis, a new approach based on Nonlinear Dynamics will be required to characterize the unstable regimes in lean gas-turbine combustors. With such approach, one may avoid the risk of misunderstanding the Deterministic Chaos, underlying in the measured signals also during stable combustion regimes, as stochastic noise. The preserved information will be thus available to analytically formulate an index acting as the earliest warning signal of an impending oscillatory combustion instability.
In the light of this, we have applied the Interdependence Index E, based on chaotic synchronization theory, to pressure and radiant energy signals sampled from an industrial combustor. The index was found: 1) low computationally demanding, since based on quantities already calculated for the phase space reconstruction; 2) really effective in the early detection of self sustained (chaotic or not) thermo-acoustic oscillations; 3) valid for a range of coupling strength, and thus smoothly increasing at the instability onset, as requested by the control system time response; 4) unaffected by the non linear relationship between heat release an chemiluminescence, that may make invalid the pseudo-Rayleigh index, computed from pressure and radiant energy fluctuations; 5) asymmetric and thus able to identify the driven and driver (sub)systems, as in combustion instabilities with no thermo-acoustic feed-back.
Application of a three-step approach for prediction of combustion instabilities in industrial gas turbine burners
