Bifurcation Analysis of Self-excited Thermoacoustic Oscillations in Damper-equipped Combustion Chambers

This paper presents the stability and bifurcation analysis of a nonlinear thermoacoustic model consisting of a combustion chamber coupled to a Helmholtz damper. Only the acoustic mode in the cavity of the combustion chamber to which the Helmholtz damper is tuned is considered. The Helmholtz damper includes a non-smooth damping term and can be seen as a tuned vibration absorber with a coupling on velocity level with non-vanishing gyroscopic terms. Conditions for which self-sustained pressure oscillations are present in the coupled system are derived. Furthermore, the effects of nonlinearities on the stability properties of the system are investigated using standard techniques of multibody dynamics. The bifurcation analysis shows a more rich dynamics than expected, considering that the investigated model describes the ideal case with perfectly tuned eigenfrequencies of the subsystems. The bifurcation branches of the occurring Hopf and fold bifurcations can be used to define a partition of the parameter space with different qualitative behaviour. The theoretical results are validated using numerical simulations.