Deterministic quantities characterizing noise driven Hopf bifurcations in gas turbine combustors

Lean premix gas turbine combustors are prone to high amplitude pressure oscillations driven by non-linear thermoacoustic coupling. These pulsations are unwanted because they can affect the lifetime of the combustor parts. The standard strategy to get rid of these oscillations is to implement acoustic damping devices. Knowing the deterministic components characterizing the acoustic-flame coupling, the linear growth rates in particular, is necessary to properly design the dampers. However, the time scale associated with the variations of the engine operating conditions is much larger than the one of the acoustic pressure amplitude dynamics. Therefore, the linearly unstable system cannot be observed during the exponential amplitude growth of one of the acoustic eigenmodes and it is not possible to directly determine the linear growth rates. They can only be estimated from signals recorded when the system is operating on limit cycling states. Fortunately, these states are driven by a strong stochastic forcing produced by the highly turbulent reactive flow. It is shown in this article that the deterministic quantities can be extracted from the noise perturbed limit cycles data by making use of the stochastic differential equations describing the combustion instabilities. A straightforward experimental set-up allowing to reproduce the main features of the thermoacoustic coupling observed in gas turbines is used to validate the proposed identification methods. In a second step, these latter methods are applied to engine data. (c) 2012 Alstom (Schweiz) AG Power Systems. Published by Elsevier Ltd. All rights reserved.