Open-loop control of periodic thermoacoustic oscillations: Experiments and low-order modelling in a synchronization framework

Abstract

Open-loop forcing is known to be an effective strategy for controlling self-excited thermoacoustic oscillations, but the details of this synchronization process have yet to be comprehensively explored. In this study, we experimentally examine the synchronization dynamics of a laminar conical premixed flame in a tube combustor subjected to periodic acoustic forcing. We compare the response of this forced self-excited system with that of a forced Duffing–van der Pol oscillator, and find many similarities but also some differences. The similarities include (i) a torus-birth bifurcation from periodicity to quasiperiodicity at low forcing amplitudes, producing a stable ergodic T2 torus attractor in phase space; (ii) a transition from T2 quasiperiodicity to lock-in above a critical forcing amplitude, which increases linearly as the forcing frequency ff deviates from the natural frequency f1; (iii) two distinct routes to lock-in, one via a torus-death bifurcation if ff is far from f1 and one via a saddle-node bifurcation if ff is close to f1; and (iv) asynchronous quenching (AQ), which coincides with a torus-death bifurcation to lock-in and reduces the oscillation amplitude – by up to 90% in the combustor. There are, however, quantitative differences between the two systems, which pertain mainly to (i) the magnitude of the amplitude reduction achieved by AQ and (ii) the size of the AQ region in the ff/f1–forcing-amplitude plane.This study has three main contributions. First, it shows that studying open-loop control from a synchronization perspective can provide valuable insight into the optimal forcing conditions. Second, it shows that the optimal forcing condition for weakening thermoacoustic oscillations is that which causes the onset of lock-in via a torus-death bifurcation, as this is where AQ occurs. Third, it shows that the synchronization dynamics of a real combustor can be qualitatively modelled with a low-order universal oscillator. This suggests that it may be possible to develop and test new control strategies by analyzing the solutions to such an oscillator.