Forced synchronization of thermoacoustic oscillations in a ducted flame*

Forced synchronization is a process in which a self-excited system subjected to external forcing starts to oscillate at the forcing frequency $f_f$ in place of its own natural frequency $f_n$. There are two motivations for studying this in thermoacoustics: (i) to determine how external forcing could be used to control thermoacoustic oscillations, which are harmful to many combustors; and (ii) to better understand the nonlinear interactions between self-excited hydrodynamic and thermoacoustic oscillations. In this experimental study, we examine the response of a ducted premixed flame to harmonic acoustic forcing, for two natural states of the system: (1) a state with periodic oscillations at $f_1$ and a marginally stable mode at $f_2$; and (2) a state with quasiperiodic oscillations at two incommensurate frequencies $f_1$ and $f_2$. When forcing the periodic state, we find that the forcing amplitude required for lock-in increases linearly with $|f_f-f_1|$ and that the marginally stable mode becomes excited when $f_f\approx f_2$. When forcing the quasiperiodic state, we find that the system locks into the forcing when $f_f\approx f_1$ or $f_2$ or $1/2(f_1+f_2)$. These findings should lead to improved control of periodic and aperiodic thermoacoustic oscillations in combustors.