The influence of the introduction of a Helmholtz resonator as a passive damper in a gas turbine combustion chamber on the bifurcation mechanism that characterizes the transition to instability is investigated. Bifurcation diagrams are tracked in order to identify the conditions for which the machine works in a stable zone and which are the operative parameters that bring the machine to unstable conditions. This work shows that a properly designed passive damper system increases the stable zone, moving the unstable zone and the bistable zone (in the case of a subcritical bifurcation) to higher values of the operative parameters, while have a limited influence on the amplitude of limit cycle. In order to examine the effect of the damper, a gas turbine combustion chamber is first modeled as a simple cylindrical duct, where the flame is concentrated in a narrow area at around one quarter of the duct. Heat release fluctuations are coupled to the velocity fluctuations at the entrance of the combustion chamber by means of a nonlinear correlation. This correlation is a polynomial function in which each term is an odd-powered term. The corresponding bifurcation diagrams are tracked and the passive damper is designed in order to increase the stability zone, so reducing the risk to have an unstable condition. Then both plenum and combustion chamber are modeled with annular shape and the influence of Helmholtz resonators on the bifurcation is examined.
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