Stability Analysis of Thermoacoustic Coupling in Damper-Equipped Combustion Chambers Including Nonlinearities
Creators: name: Baumann, Michael
Publisher: name: ETH Zurich
Year: 2013
Subjects: COMBUSTION CHAMBERS (GAS TURBINES)
THERMISCHE SCHWINGUNGSERREGUNG (AKUSTIK)
KELVIN-HELMHOLTZ INSTABILITY (FLUID DYNAMICS)
DAMPING OF MECHANICAL OSCILLATIONS (ACOUSTICS)
KELVIN-HELMHOLTZ INSTABILITÄT (FLUIDDYNAMIK)
BRENNKAMMERN (GASTURBINEN)
DÄMPFUNG MECHANISCHER SCHWINGUNGEN (AKUSTIK)
THERMAL EXCITATION OF VIBRATIONS (ACOUSTICS)
info:eu-repo/classification/ddc/620
Engineering &amp; allied operations

description: Combustion chambers of gas turbines can be viewed as organ pipes in which acoustic pressure and velocity oscillations can be sustained. Thermoacoustic instabilities can occur due to thermoacoustic coupling between the flame and the pressure oscillations. Acoustic resonators such as Helmholtz dampers are commonly used to increase the acoustic dissipation and abate the severe pressure oscillations. Yet, it remains a challenging task to derive conditions which promote the potential coupling. In order to predict the damper performance, a theoretical model combining the combustion instability and the damper dynamics is derived by Nicolas Noiray and Bruno Schuermans [9] from ALSTOM Power. The model consists of two nonlinear coupled differential equations of second order. The first equation describes the acoustic pressure oscillation in the combustor of one particular acoustic mode. The linear growth rate is captured by a linear damping term, whereas the boundedness of the solutions are ensured by a nonlinear damping term. The second equation describes the acoustic velocity oscillation in the neck of the Helmholtz damper, which includes a non-smooth damping term. The acoustic absorption is maximized when the eigenfrequency of the damper is adjusted to the unstable mode of the combustor. This special case is referred to as the perfectly tuned model, which is a special case of the general model including static detuning. The objective of this project is the nonlinear analysis of these models. The stability of the equilibrium is determined by an eigenvalue analysis and the region of attraction is approximated with the use of Lyapunov techniques. Due to the nonlinearities present in the system, several periodic solutions exist, which are approximated using three different methods from nonlinear dynamics, which are the center manifold reduction, the method of multiple scales and the method of averaging. The bifurcation analysis of the perfectly tuned model shows a wider range of dynamics than expected. Additionally to a supercritical Hopf bifurcation, also fold bifurcations and a cusp catastrophe can occur. The bifurcation branches define a partition of the parameter space into four regions of which every region has a different number of limit sets. The model with static detuning shows a similar behaviour. The pressure in the combustion chamber and the acoustic velocity in the neck of the Helmholtz damper oscillate at the same frequency. Yet, which is in contrast to the perfectly tuned model, there exists a phase shift between the oscillations and the frequency of oscillation depends on the bifurcation parameter.