Synchronization of thermoacoustic quasiperiodic oscillation by periodic external force

Abstract

Quasiperiodic oscillations can occur in nonequilibrium systems where two or more frequency components are generated simultaneously. Many studies have explored the synchronization of periodic and chaotic oscillations; however, the synchronization of quasiperiodic oscillations has not received much attention. This study experimentally documents forced synchronization of the quasiperiodic state and the internally locked state of a thermoacoustic oscillator system. This system consists of a gas-filled resonance tube with a nonuniform cross-sectional area. The thermoacoustic oscillator was designed and built in such a way that nonlinear interactions between the fundamental acoustic oscillation mode and the third mode of the gas column are controlled by a temperature difference that is locally created in the resonance tube. Bifurcation diagrams were mapped out by changing the forcing strength and frequency. Separated Arnold tongues were found and both modes were entrained to the external force through complete synchronization. A saddle-node bifurcation was observed in the route from partial to complete synchronization when the forcing strength was relatively weak. However, a Hopf (torus-death) bifurcation was observed when the forcing was relatively strong. In the internally locked state, the bifurcation occurred after the internal locking was broken down by the external force.

Mutual synchronization of self-excited acoustic oscillations in coupled thermoacoustic oscillators

“…It refers to the process in which the TAE oscillates not at its own natural frequency, but at the frequency of a periodic external force or another TAE. Synchronization of a TAE by an external force has been reported by Penelet [24] and Sato [25]. In Ref.…”

Rijke tube: A nonlinear oscillator

“…In an experimental study, Mondal et al 119 examined forced synchronization of limit cycle oscillations in the acoustic pressure of a horizontal Rijke tube system, while Guan et al 286 and Roy et al 287 investigated forced synchronization of limit cycle oscillations in both the acoustic pressure and heat release rate fluctuations of a laminar premixed flame Rijke tube burner. Furthermore, Guan et al 286 and Sato et al 288 extended the experimental investigation to study forced synchronization of quasiperiodic oscillations in a laminar premixed flame Rijke tube burner and a gas filled resonance tube, respectively. In a different study, Sahay et al 274 examined forced synchronization of two coupled identical and nonidentical horizontal Rijke tube oscillators with forcing being applied to one of the oscillators, both experimentally and numerically.…”

“…The combined behavior of the two spectral amplitudes is observed in the variation of the rms value of the response pressure signal (P rms /P 0 rms ). Unlike forced synchronization of limit cycle oscillations, forced synchronization of quasiperiodic oscillations happens via a complicated path and involves various variants of quasiperiodic oscillations 286,288 . The system first transitions from quasiperiodic oscillations having two dominant frequencies to another variant of quasiperiodic oscillations having three dominant frequencies (two natural frequencies and one forcing frequency).…”

Nonreciprocal and even Willis couplings in periodic thermoacoustic amplifiers

“…Although research in thermoacoustics has mostly been * jean-philippe.groby@univ-lemans.fr oriented towards the development of thermodynamic machines and the understanding of the phenomena controlling their behavior-on the one hand, the thermoacoustic prime movers (or engines) [12,13]; on the other hand, thermoacoustic heat pumps and refrigerators [14,15]-more fundamental research has relied on the thermoacoustic amplification or damping of acoustic waves in recent years. Quasiperiodic and chaotic oscillations [16,17] or synchronization phenomena involved in thermally driven autonomous oscillators [18,19], thermoacoustic shock waves [20,21], and solitary waves [22], thermoacoustic diode [8], or a PT -symmetric system [23] have been the focus of a growing interest. Thermoacoustics still appears to be overlooked as far as nonreciprocal systems are concerned.…”