## Abstract

In self-excited combustion systems, the application of open-loop forcing is known to be an effective strategy for controlling periodic thermoacoustic oscillations, but it is not known whether and under what conditions such a strategy would work on thermoacoustic oscillations that are not simply periodic. In this study, we experimentally examine the effect of periodic acoustic forcing on a prototypical thermoacoustic system consisting of a ducted laminar premixed flame oscillating quasiperiodically on an ergodic torus at two incommensurate natural frequencies, and. Compared with that of a classical period-1 system, complete synchronization of this system is found to occur via a more intricate route involving three sequential steps: As the forcing amplitude, , increases at a fixed forcing frequency, , the system transitions first (i)to ergodic quasiperiodicity; then (ii)to resonant quasiperiodicity as the weaker of the two natural modes, , synchronizes first, leading to partial synchronization; and finally (iii)to a limit cycle as the remaining natural mode, , also synchronizes, leading to complete synchronization. The minimum required for partial and complete synchronization decreases as approaches either or , resulting in two primary Arnold tongues. However, when forced at an amplitude above that required for complete synchronization, the system can transition out of and into or . The optimal control strategy is to apply off-resonance forcing at a frequency around the weaker natural mode and at an amplitude just sufficient to cause , because this produces the largest reduction in thermoacoustic amplitude via asynchronous quenching. Analysis of the Rayleigh index shows that this reduction is physically caused by a disruption of the positive coupling between the unsteady heat release rate of the flame and the and acoustic modes. If the forcing is applied near the stronger natural mode , however, resonant amplification can occur. We then phenomenologically model this thermoacoustic system as two reactively coupled van der Pol oscillators subjected to external sinusoidal forcing, and find that many of its synchronization features-such as the three-step route to , the double Arnold tongues, asynchronous quenching and resonant amplification-can be qualitatively reproduced. This shows that these features are not limited to our particular system, but are universal features of forced self-excited oscillators. This study extends the applicability of open-loop control from classical period-1 systems with just a single time scale to ergodic quasiperiodic systems with two incommensurate time scales.

Original language | English |
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Pages (from-to) | 390-421 |

Number of pages | 32 |

Journal | Journal of Fluid Mechanics |

Volume | 879 |

DOIs | |

Publication status | Published - 25 Nov 2019 |

Externally published | Yes |

## Keywords

- Instability control
- Nonlinear instability

## ASJC Scopus subject areas

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering