Bursting and mixed mode oscillations during the transition to limit cycle oscillations in a matrix burner

Abstract

We investigate the route to self-excited thermoacoustic instability in a laminar flow multiple flame matrix burner. With an increase in the equivalence ratio, the thermoacoustic system that is initially quiet (stable operation) transitions to limit cycle oscillations through two distinct dynamical states, namely, bursting oscillations and mixed mode oscillations. The acoustic pressure oscillations transition from quiescence to large amplitudes during bursting oscillations. Such high amplitude bursting oscillations that occur well ahead of the onset of limit cycle oscillations can potentially cause structural damage. The thermoacoustic system exhibits hysteresis. The transition to limit cycle oscillations is replicated in a phenomenological model containing slow-fast time scales.

Rijke tube: A nonlinear oscillator

“…The amplitude-modulated oscillations were accompanied by low frequency flame pulsations having a frequency lower than 1 Hz; thereby, creating a time scale difference of 10 2 − 10 3 between the pulsations in the flame and the thermoacoustic oscillations. Subsequently, Kasthuri et al 113 observed the presence of bursting and mixed-mode oscillations in a premixed matrix burner with several interacting laminar flames (Fig. 8c).…”

“…The fuel-air mixture is ignited in the system using a spark plug or a small pilot flame. In this setup, we can study the interaction of the acoustic field with different configurations of laminar flames including conical flame 109,110 , V-flame 75,111,112 , and also multiple conical flames 109,112,113 .…”

“…Unlike direct transitions observed from steady state to thermoacoustic instability through Hopf bifurcation in the previous subsections, we come across a few studies on Rijke tube systems that report the transition to occur via an intermediate dynamical state. Various types of oscillatory dynamics such as intermittency 117 , bursting 106,113 , beating 171 , and mixed-mode oscillations 113 have been observed as the intermediate state in different Rijke tube systems. Intermittency is characterized by the occurrence of bursts of high amplitude periodic oscillations amidst epochs of low amplitude aperiodic ones.…”

“…8. Different types of intermediate states observed in acoustic pressure fluctuations (p ) during the transition from steady state to limit cycle oscillations such as (a) intermittency in the spray combustor 117 , (b) beating dynamics in the Rijke-type burner 171 , (c) bursting in the multiple flames matrix burner 113 , and (d) bursting in the horizontal Rijke tube 106 . Reproduced with permission from Tandon et al 106 .…”

Synchronization framework for modeling transition to thermoacoustic instability in laminar combustors

“…Kabiraj et al [21] investigated various bifurcations in a laminar thermoacoustic system and established a route from self-excited periodic oscillation to chaos via the Ruelle-Takens scenario. Kasturi et al [22] discovered bursting oscillations and mixed mode oscillation in a laboratory combustor with a matrix flame. Intermittent oscillations were also observed in a thermoacoustic system as the system transitioned between a state of periodic oscillations to flame extinction [23].…”