Open-loop control of quasiperiodic thermoacoustic oscillations

The open-loop application of periodic acoustic forcing has been shown to be a potentially effective strategy for controlling periodic thermoacoustic oscillations, but its effectiveness on aperiodic thermoacoustic oscillations is less clear. In this experimental study, we apply periodic acoustic forcing to a ducted premixed flame oscillating quasiperiodically at two incommensurate natural frequencies, $f_1$ and $f_2$. We find that (i) above a critical forcing amplitude, the system locks into the forcing by oscillating only at the forcing frequency $f_f$, producing a closed periodic orbit in phase space with no evidence of the original ${\mathbb{T}}^2$ torus attractor; (ii) the critical forcing amplitude required for lock-in decreases as $f_f$ approaches either $f_1$ or $f_2$, resulting in characteristic $\vee$-shaped lock-in boundaries around the two natural modes; and (iii) for a wide range of forcing frequencies, the system's oscillation amplitude can be reduced to less than 20\% of that of the unforced system. These findings show that the open-loop application of periodic acoustic forcing can be an effective strategy for controlling aperiodic thermoacoustic oscillations.