Influence of nonlinear flame models on sustained thermoacoustic oscillations in gas turbine combustion chambers

In the recent years a great interest has been devoted to the understanding of the nonlinear dynamics characterizing the thermoacoustic combustion instabilities. Although linear techniques are able to predict whether the non-oscillating steady state of a thermoacoustic system is “asymptotically” stable (without oscillations) or unstable (increasing oscillations), a thermoacoustic system can reach a permanent oscillating state (the so called “limit cycle”), even when it is linearly stable, if a sufficiently large impulse occurs. A nonlinear analysis is able to predict the existence of this oscillating state and the nature of the bifurcation process. The aim of this work is to investigate the behavior of gas turbine combustion chambers in presence of nonlinear flame models. The bifurcation diagrams, obtained by using a continuation technique in the frequency domain, give the amplitude of the oscillations as a function of a chosen flame parameter. The Helmholtz equation is used to model the combustion chamber and nonlinear terms are introduced in the flame model, starting from the classical k–τ formulation. A three-dimensional finite element method (FEM) is used for discretization of the computational domain and a solver of quadratic eigenvalue problems is combined with Newton technique in order to identify the points of the bifurcation diagram. First, a simple Rijke tube configuration, as can be found in the literature, is examined in order to obtain bifurcation diagrams. Then, the nonlinear analysis is extended to simplified annular configurations. The obtained results show how the nonlinear behavior is influenced by varying some control parameters, such as the time delay, yielding useful indications to designers and experimentalists.